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A word is called a palindrome if it is equal to its reversal. In the paper we consider a k -abelian modification of this notion. Two words are called k - abelian equivalent if they contain the same number of occurrences of each factor of length at most k . We say that a word is a k - abelian palindrome if it is k -abelian equivalent to its reversal. A question we deal with is the following: how many distinct palindromes can a word contain? It is well known that a word of length n can contain at most n + 1 distinct palindromes as its factors; such words are called rich . On the other hand, there exist infinite words containing only finitely many distinct palindromes as their factors; such words are called poor . We show that in the k -abelian case there exist infinite words containing finitely many distinct k -abelian palindromic factors. For rich words we show that there exist finite words of length n containing Θ ( n 2 ) distinct k -abelian palindromes as their factors. [ABSTRACT FROM AUTHOR]

Let be the dihedral group of order , where is an odd prime. A nonempty subset of is said to be exhaustive if there exists a positive integer such that covers all elements in . The smallest such is called the exhaustion number of . In general, finding for an arbitrary subset of is an interesting but difficult task. In this paper, we classify all possible exhaustion 2-subsets in by considering a 2-subset of with either or and . Some explicit formulas for are identified and hence some bounds are derived to prove the existence for certain families of exhaustive sets. [ABSTRACT FROM AUTHOR]

We find the groups of motions of eight three-dimensional maximal mobility geometries. These groups are actions of just three Lie groups SL2(R)ΔN, SL2(C)R, and SL2(R)⊗SL2(R) on the space R3, where N is a normal abelian subgroup. We also find explicit expressions for these actions. [ABSTRACT FROM AUTHOR]

In this paper, we give a new class of association schemes whose thin residues are isomorphic to an elementary abelian p -group of order p 2 . We then study the automorphism groups of these schemes and determine whether these schemes are schurian. [ABSTRACT FROM AUTHOR]

A p-group G is called a C AC-p-group if CG(H)/H is cyclic for every non-cyclic abelian subgroup H in G with H ≰ Z(G). In this paper, we give a complete classification of finite C AC-p-groups. [ABSTRACT FROM AUTHOR]

In the paper, it is established that every hereditary hyperradical formation is saturated, and a description of all hereditary hyperradical formations is given. [ABSTRACT FROM AUTHOR]

The first example of a torsion-free abelian group $(A,+,0)$ such that the quotient group of $A$ modulo the square subgroup is not a nil-group is indicated (for both associative and general rings). In particular, the answer to the question posed by Stratton and Webb [‘Abelian groups, nil modulo a subgroup, need not have nil quotient group’, Publ. Math. Debrecen27 (1980), 127–130] is given for torsion-free groups. A new method of constructing indecomposable nil-groups of any rank from $2$ to $2^{\aleph _{0}}$ is presented. Ring multiplications on $p$-pure subgroups of the additive group of the ring of $p$-adic integers are investigated using only elementary methods. [ABSTRACT FROM PUBLISHER]

We prove that the radial subalgebra in free orthogonal quantum group factors is maximal abelian and mixing, and we compute the associated bimodule. The proof relies on new properties of the Jones–Wenzl projections and on an estimate of certain scalar products of coefficients of irreducible representations. [ABSTRACT FROM AUTHOR]

We give an explicit construction of infinite sharply 2-transitive groups with fixed point free involutions and without nontrivial abelian normal subgroup. [ABSTRACT FROM AUTHOR]

In this note, we prove an adelic open image theorem for abelian schemes and, more generally, families of 1-motives.This result, which can be interpreted as an adelic specialization theorem, shows for instance the abundancy of Galois-generic closed points on most connected Shimura varieties. [ABSTRACT FROM AUTHOR]

LetAbe an abelian variety over ℂ such that the semisimple part of the Hodge group ofAis a product of copies ofSU(p, 1) for somep > 1. We show that any effective Tate twist of a Hodge structure occurring in the cohomology ofAis isomorphic to a Hodge structure in the cohomology of some abelian variety. [ABSTRACT FROM AUTHOR]

We obtain a description of quasi-endomorphism rings of almost completely decomposable torsion-free Abelian groups of rank 4 that do not coincide with their pseudo-socles. [ABSTRACT FROM AUTHOR]

We compute the elliptic genera of general two-dimensional $${\mathcal{N} = (2, 2)}$$ and $${\mathcal{N} = (0, 2)}$$ gauge theories. We find that the elliptic genus is given by the sum of Jeffrey-Kirwan residues of a meromorphic form, representing the one-loop determinant of fields, on the moduli space of flat connections on T. We give several examples illustrating our formula, with both Abelian and non-Abelian gauge groups, and discuss some dualities for U( k) and SU( k) theories. This paper is a sequel to the authors' previous paper (Benini et al., Lett Math Phys 104:465-493, ). [ABSTRACT FROM AUTHOR]

The notion of a generic theory GTh( $$ \mathcal{K} $$, μ) with respect to a measure μ was introduced in [Algebra and Logic, 53, No. 6, 512-519 (2014)]. Here, generic theories for two series of cyclic groups are described based on elementary invariants for Abelian groups and using a measure generated by a Frechet filter. Axioms of generic theories are given, complete theories are characterized in terms of elementary invariants, and canonical models of complete theories are constructed. [ABSTRACT FROM AUTHOR]

Let $$X$$ be a finite CW complex. We say that $$X$$ is large if $$X$$ has a finite cover $$Y$$ whose fundamental group surjects to a non-abelian free group. We show that the fundamental group of $$X$$ is large if and only if there is a finite cover $$Y$$ of $$X$$ and a sequence of finite abelian covers $$\{Y_N\}$$ of $$Y$$ which satisfy $$b_1(Y_N)\ge N$$. We give some applications of this result to the study of hyperbolic $$3$$-manifolds, mapping classes of surfaces and combinatorial group theory. [ABSTRACT FROM AUTHOR]

Abstract: Let G be a finite (not necessarily abelian) group and let be the smallest prime number dividing . We prove that , where denotes the small Davenport constant of G which is defined as the maximal integer ℓ such that there is a sequence over G of length ℓ containing no nonempty one-product subsequence. [Copyright &y& Elsevier]

We give a description of real equivariant bordism for the group G = ℤ x ... x ℤ/2, which is similar to the description of complex equivariant bordism for the group S¹ x ... x S¹ given by Hanke in [Han05, Theorem 1]. [ABSTRACT FROM AUTHOR]

In our earlier paper it was proved that the singular locus of Ag (coarse moduli space of principally polarized abelian varieties over C) is expressed as the union of irreducible varieties Ag(p, a) representing abelian varieties with an order p automorphism of fixed entire representation. In this paper we prove that Ag(p, α) is an irreducible component of SingAg if and only if for a general element of this variety its automorphism group modulo {±1}, G+, satisfies the equivalent conditions: G+ = _a_ or NG+(_a_) = _a_. We illustrate how these results can be used by studying the case g = 4 and p = 5. [ABSTRACT FROM AUTHOR]

The article examines the isogeny classes of abelian surfaces over Fq whose group of Fq-rational points contains order divisible by q2. It also examines the same problem for Jacobians of genus-2 curves. It discusses the Frobenius endomorphism as well as the Weil polynomials of abelian varieties.

The article examines the isogeny classes of abelian surfaces over Fq whose group of Fq-rational points contains order divisible by q2. It also examines the same problem for Jacobians of genus-2 curves. It discusses the Frobenius endomorphism as well as the Weil polynomials of abelian varieties.

We construct a non-abelian extension Γ of S1 by Z/3 × Z/3, and prove that Γ acts freely and smoothly on S5 × S5. This gives new actions on S5 × S5 for an infinite family  of finite 3-groups. We also show that any finite odd-order subgroup of the exceptional Lie group G2 admits a free smooth action on S11 × S11. This gives new actions on S11 × S11 for an infinite family ℰ of finite groups. We explain the significance of these families , ℰ for the general existence problem, and correct some mistakes in the literature. [ABSTRACT FROM PUBLISHER]

Let G be a finite group and let δ(G) be the number of prime order subgroups of G. We determine the groups G with the property δ(G) > ∣G ∣/2 - 1, extending earlier work of C. T. C. Wall, and we use our classification to obtain new results on the generation of near-rings by units of prime order. [ABSTRACT FROM AUTHOR]

We characterize the Lebesgue state of a free finitely generated unital lattice-ordered abelian group G in terms of its value at each element of each basis of G. This significantly strengthens one of the main results of our previous paper (co-authored by D. Mundici) with the same title as the present one. As a consequence of independent interest, we obtain a state-theoretic characterization of free finitely generated objects in the category of unital lattice-ordered abelian groups and their unit-preserving lattice-group homomorphisms. [ABSTRACT FROM AUTHOR]

Let G be a finite group with a non-central Sylow r-subgroup R, Z( G) the center of G, and N a normal subgroup of G. The purpose of this paper is to determine the structure of N under the hypotheses that N contains R and the G-conjugacy class size of every element of N is either 1 or m. Particularly, it is shown that N is Abelian if N ∩ Z( G) = 1 and the G-conjugacy class size of every element of N is either 1 or m. [ABSTRACT FROM AUTHOR]

We show that is finite of order (mi)!(i!)m−2 and that is free abelian of rank m − 1. This is accomplished by showing that the equivariant homotopy groups of the topological Hochschild -spectrum are free abelian for q even, and finite for q odd, and by determining their ranks and orders, respectively. [ABSTRACT FROM PUBLISHER]

In this article, we consider the Jordanian plane over a field of arbitrary characteristic. We describe the prime spectrum, the group of automorphisms, and derivations of the Jordanian plane. We study some properties of valuations of the Jordanian plane. In particular, we prove that all valuations of the division ring of fractions of the Jordanian plane are Abelian. [ABSTRACT FROM AUTHOR]

Abstract: Throughout, all rings will be commutative with identity element. In this paper we introduce, for each finite group , a commutative graded -algebra . This classifies the -invariant commutative -algebra multiplications on the group algebra which are cocycles (in fact coboundaries) with respect to the standard “direct sum” multiplication and have the same identity element. In the case when is an elementary Abelian -group it turns out that is closely related to the symmetric algebra over of the dual of . We intend in subsequent papers to explore the close relationship between and in the case of a general (possibly non-Abelian) group . Here we show that the Krull dimension of is the maximal rank of an elementary Abelian subgroup of unless either is cyclic or for some such its normalizer in contains a non-trivial cyclic group which acts faithfully on via “scalar multiplication” in which case it is . [Copyright &y& Elsevier]

The just non-(virtually abelian) groups with non-trivial Fitting subgroup are classified. Particular attention is given to those which are virtually nilpotent and examples are given of the interesting phenomena that can occur. [ABSTRACT FROM PUBLISHER]

A proper short exact sequence in the category of locally compact abelian groups is said to be t-pure if φ(A) is a topologically pure subgroup of B, that is, if for all positive integers n. We establish conditions under which t-pure exact sequences split and determine those locally compact abelian groups K ⊕ D (where K is compactly generated and D is discrete) which are t-pure injective or t-pure projective. Calling the extension (*) almost pure if for all positive integers n, we obtain a complete description of the almost pure injectives and almost pure projectives in the category of locally compact abelian groups. [ABSTRACT FROM AUTHOR]

Abstract: Edmonds showed that two free orientation preserving smooth actions and of a finite Abelian group G on a closed connected oriented smooth surface M are equivalent by an equivariant orientation preserving diffeomorphism iff they have the same bordism class in the oriented bordism group of the group G. In this paper, we compute the bordism class for any such action of G on M and we determine for a given M, the bordism classes in that are representable by such actions of G on M. This will enable us to obtain a formula for the number of inequivalent such actions of G on M. We also determine the “weak” equivalence classes of such actions of G on M when all the p-Sylow subgroups of G are homocyclic (i.e. of the form . [Copyright &y& Elsevier]

An appropriate definition of the Hodge duality ⋆ operation on any arbitrary dimensional supermanifold has been a long-standing problem. We define a working rule for the Hodge duality ⋆ operation on the (2+2)-dimensional supermanifold parametrized by a couple of even (bosonic) space–time variables xμ(μ = 0, 1) and a couple of odd (fermionic) variables θ and $\bar\theta$ of the Grassmann algebra. The Minkowski space–time manifold, hidden in the supermanifold and parametrized by xμ(μ = 0, 1), is chosen to be a flat manifold on which a two (1+1)-dimensional (2D) free Abelian gauge theory, taken as a prototype field theoretical model, is defined. We demonstrate the applications of the above definition (and its further generalization) for the discussion of the (anti-)co-BRST symmetries that exist for the field theoretical models of 2D and 4D free Abelian gauge theories considered on the four (2+2)- and six (4+2)-dimensional supermanifolds, respectively. [ABSTRACT FROM AUTHOR]

There is a simple group-theoretic formula for the second integral homology group of a group. This is an abelian group and there is an analogous formula for another abelian group, which involves a normal subgroup N of a torsion-free nilpotent group G. Properties of this abelian group translate into properties of G/N. This approach allows one to give a simple purely group-theoretic proof of an old theorem of J. R. Stallings, namely that if Γ is a group, if H1(G,ℤ) is free abelian and if H2(G,ℤ) = 0, then any subset Y of G which is independent modulo the derived group of G, freely generates a free group. The ideas used admit to considerable generalization, yielding in particular, proofs of a number of theorems of U. Stammbach. [ABSTRACT FROM AUTHOR]

Abstract: We prove that direct and inverse limits of sequences of reflexive Abelian groups that are metrizable or -spaces, but not necessarily locally compact, are reflexive and dual of each other provided some extra conditions are satisfied by the sequences. [Copyright &y& Elsevier]

Abstract: We define a certain quotient of the étale fundamental group of a scheme which classifies étale coverings with bounded ramification along the boundary, and show the finiteness of the abelianization of this group for an arithmetic scheme. To cite this article: T. Hiranouchi, C. R. Acad. Sci. Paris, Ser. I 341 (2005). [Copyright &y& Elsevier]

If G is a nontrivial finite group with the property that ?(1) 2 divides bi | G | for all irreducible (complex) characters ?, then G has a nontrivial normal abelian subgroup. [ABSTRACT FROM AUTHOR]

In this paper we prove that the pseudovariety of Abelian groups is hyperdecidable and moreover that it is completely tame. This is a consequence of the fact that a system of group equations on a free Abelian group with certain rational constraints is solvable if and only if it is solvable in every finite quotient. [ABSTRACT FROM AUTHOR]

We establish a uniqueness result for the topological multivortex solution to the self-dual equations of the Abelian relativistic self-dual Chern–Simons–Higgs model. We prove that the topological multivortex solution is unique if the Chern–Simons coupling parameter κ>0 is sufficiently small. We also establish a uniqueness result for κ>0 sufficiently large. [ABSTRACT FROM AUTHOR]

We say that a ring R satisfies unit 1-stable range if a R + bR = R implies that a + bu ∈ U(R) for a u ∈ U(R). These rings are shown to be a natural generalization of the rings satisfying the Goodearl-Menal condition. It is shown that if R is an abelian ring satisfying unit 1-stable range, then K1(R) ≅ U(R)ab [ABSTRACT FROM AUTHOR]

A formula for computing the discriminant of any number field K ⊂ ℚ(ζ[sub 2[sup r]]), with r ≥ 3, is derived. The formula consists of two expressions, depending on whether K is cyclotomic or not. However, both expressions depend solely on m, the degree of K over ℚ, and they are derived from the Conductor-Discriminant Formula for Abelian extensions of ℚ. [ABSTRACT FROM AUTHOR]

First, we present a simple confining abelian pure gauge theory. Classically, its kinetic term is not positive definite, and it contains a simple LIV regularized F4 interaction. This provokes the formation of a condensate φ ∼ F2 such that, at the saddle point φ of the effective potential, the wave function normalization constant of the abelian gauge fields Zeff (φ) vanishes exactly. Then we study SU(2) pure Yang-Mills theory in an abelian gauge and introduce an auxiliary field ρ for a BRST invariant condensate of dimension 2, which renders the charged sector massive. Under simple assumptions its effective low energy theory reduces to the confining abelian model discussed before, and the VEV of ρ is seen to scale correctly with the renormalization point. Under these assumptions, the confinement condition Zeff = 0 also holds for the massive charged sector, which suppresses the couplings of the charged fields to the abelian gauge bosons in the infrared regime. [ABSTRACT FROM AUTHOR]

We prove that every group with nilpotent commutant, having an abelian normal subgroup such that the factor by this subgroup is nilpotent, is preorderable if and only if the group is Γ-torsion-free. An example is exhibited of a nonorderable Γ-torsion-free group with two-step nilpotent radical. This example demonstrates that for the variety of groups with nilpotent commutant the absence of Γ-torsion in a group is not a sufficient condition for orderability. [ABSTRACT FROM AUTHOR]

The method of Abelian decomposition proposed by Faddeev and Niemi is used to derive the low-energy effective lagrangian of G2 gauge theory. The G2 algebra is studied. The commutation relations among the generators of the G2 algebra are established, based on the framework of its regular maximal subalgebra, an SU(3) algebra. [ABSTRACT FROM AUTHOR]

Let p be an odd prime, let G be a finite Abelian group, and let A (G) denotes the automorphism group of G. In this paper, using method of elementary number theory, it is proved that if ∣A(G)∣ = 26p2 ,where p ≠ 3, 5 or 17, then C has at most 20 types. [ABSTRACT FROM AUTHOR]