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In this paper, we prove an Artin type theorem for semigroups. Namely, we consider the concepts of hyperalternative and hyperassociative semigroups and prove that every two elements in any hyperalternative semigroup generate a hyperassociative subsemigroup. As a consequence, we characterize all hyperalternative semigroups, and prove that these semigroups form a variety of semigroups with four identities. [ABSTRACT FROM AUTHOR]

In [H. P. Tong-Viet, Simple classical groups of Lie type are determined by their character degrees, J. Algebra 357 (2012) 61-68] the following question arose: Question. Which groups can be uniquely determined by the structure of their complex group algebras? It is proved that every quasisimple group except covers of the alternating groups is uniquely determined up to isomorphism by the structure of , the complex group algebra of . One of the next natural groups to be considered are the characteristically simple groups. In this paper, as the first step in this investigation we prove that if is an odd prime number, then is uniquely determined by the structure of its complex group algebra. [ABSTRACT FROM AUTHOR]

Groups with triality, which arose in the papers of Glauberman and Doro, are naturally connected with Moufang loops. In this paper, we describe all possible, in a sense, groups with triality associated with a given Moufang loop. We also introduce several universal groups with triality and discuss their properties. [ABSTRACT FROM AUTHOR]

In this paper, we reexamine the foundation of Isaacs' π-theory. One of the key concepts in Isaacs' π-theory is the construction of the characters Bπ(G) for a π-separable group G. The key to determining which characters lie in Bπ(G) was the construction of a nucleus for each irreducible character χ. In this paper, we present a different way of finding a nucleus for χ which is based on a chain of normal subgroup $\mathcal{N}$. Using this nucleus, we obtain the set of characters $B_{\pi}(G:\mathcal{N})$. We investigate the properties that $B_{\pi}(G:\mathcal{N})$ has in common with Bπ(G). [ABSTRACT FROM AUTHOR]

(Co)induction functors appear in several areas of Algebra in different forms. Interesting examples are the so called induction functors in the Theory of Affine Algebraic Groups. In this paper we investigate Hopf pairings (bialgebra pairings) and use them to study (co)induction functors for affine group schemes over arbitrary commutative ground rings. We present also a special type of Hopf pairings (bialgebra pairings) satisfying the so called α-condition. For those pairings the coinduction functor is studied and nice descriptions of it are obtained. Along the paper several interesting results are generalized from the case of base fields to the case of arbitrary commutative (Noetherian) ground rings. [ABSTRACT FROM AUTHOR]

A finite group G is said to be a minimal non- group if G is not a group of class ≤ n whose proper subgroups are of class ≤ n. In this paper, we give a complete classification of minimal non-p-groups G with G3 ≅ Cp × Cp for p > 3. [ABSTRACT FROM AUTHOR]

Let A be a commutative integral domain with quotient field L, and let R be a subdomain of A with quotient field K. Assuming that L is a Galois extension of K, Nagata required the condition for R to be normal when A is called a Galois extension of R (see p. 31, M. Nagata, Local Rings (Wiley, New York, 1962)). However in this paper, A is considered in the case that R is not necessarily assumed to be normal. We introduce the notion of cyclic Galois extensions of integral domains and investigate several properties of such ring extensions. In particular, we completely determine the seminormalization ${}^+_BA$ of A in an overdomain B such that both A ⊆B are cyclic Galois extensions of R. [ABSTRACT FROM AUTHOR]

This paper investigates to which extent a self-small mixed Abelian group G of finite torsion-free rank is determined by the groups Hom(G,C) where C is chosen from a suitable class $\mathcal C$ of Abelian groups. We show that G is determined up to quasi-isomorphism if $\mathcal C$ is the class of all self-small mixed groups C with r0(C) ≤ r0(G). Several related results are given, and the dual problem of orthogonal classes is investigated. [ABSTRACT FROM AUTHOR]

Let p and q be odd primes, and let G be an M-group of order paqb. Loukaki has proven that if N is a normal subgroup of G, then N is an M-group. In this paper, we present a simpler proof of Loukaki's theorem. We also present a slight generalization of Loukaki's theorem. [ABSTRACT FROM AUTHOR]

In this paper branching rules for the polynomial irreducible representations of the general linear groups in positive characteristic with highest weights labeled by partitions of the form (2a, 1b, 0c) and their restrictions to the special linear groups are found. The submodule structure of the restrictions of the corresponding irreducible modules for the group GLn(F) (or SLn(F)) to the naturally embedded subgroup GLn-1(F) (or SLn-1(F)) is determined. As a corollary, inductive systems of irreducible representations for GL∞(F) and SL∞(F) that consist of representations indicated above, are classified. The submodule structure of the relevant Weyl modules is refined. [ABSTRACT FROM AUTHOR]

A binomial f belonging to a toric ideal I is indispensable if, for any system $\mathcal{F}$ of binomial generators of I, either f or -f belongs to $\mathcal{F}$. In the present paper, we study indispensable binomials of the toric ideals IG arising from a finite graph G. First, we show that the toric ideal IG arising from a finite graph G whose complementary graph is weakly chordal is generated by the indispensable binomials if and only if no complete graph of order ≥4 is a subgraph of G. Second, we completely classify indispensable binomials of the toric ideal IG arising from a finite graph G satisfying the odd cycle condition. Finally, the existence of indispensable binomials of IG will be discussed. [ABSTRACT FROM AUTHOR]

A subnormal subgroup X of G has the following property: there exists a Dirichlet polynomial Q(s) with integer coefficients such that, for each t ∈ ℕ, Q(t) is the conditional probability that t random elements generate G given that they generate G together with the elements of X In this paper we analyze how far can a subgroup X be with this property from being a subnormal subgroup. [ABSTRACT FROM AUTHOR]

Given a compactly generated triangulated category $\mathcal{T}$ and a generating set ℛ of compact objects, the class of ℛ-injective objects $\mathsf{Inj}_\mathcal{R}\ \mathcal{T}$ is introduced. If $X\in\mathcal{T}$ is compact and ℛ={ΣnX}n∈ℤ it is shown that there is a functor \[ \Gamma:\mathsf{Inj}\ \mathcal{S} \to \mathsf{Inj}_{\mathcal R}\ \mathcal{T} \] identifying the class $\mathsf{Inj}\,\mathcal{S}$ of injective modules over the ℤ-graded ring $S=\bigoplus_{n\in\mathbb{Z}}\ \mathcal{T}(\Sigma^nX,X)$ with the class $\mathsf{Inj}_{\mathcal R}\ \mathcal{T}$. Also, the Ziegler and Zariski spectra of $\mathcal{T}$ and of S are discussed in the paper. [ABSTRACT FROM AUTHOR]

In this paper, we prove that a finite group G is isomorphic to the alternating group An with n≥5 if and only if they have the same set of the orders of solvable subgroups. [ABSTRACT FROM AUTHOR]