Search

Let N be a minimal normal subgroup of a finite group G. The aim of the present paper is to investigate the influence of the quotient group G=N on the normalizer conjecture of the integral group ring 핫G. Some conditions on G=N are obtained under which the normalizer conjecture holds for 핫G. [ABSTRACT FROM AUTHOR]

Let G be a finite cyclic group. Every sequence S over G can be written in the form S = (n1g)·...·(nig) where g ∈ G and ni,...,n¡ ∈ [l,ord(g)], and the index ind(S) of S is defined to be the minimum of (n1 + ... + n¡)/ord(g) over all possible g ∈ G such that 〈g〉 = G. An open problem on the index of length four sequences asks whether or not every minimal zero-sum sequence of length 4 over a finite cyclic group G with gcd(|G|,6) = 1 has index 1. In this paper, we show that if G = 〈g〉 is a cyclic group with order of a product of two prime powers and gcd(|G|,6) = 1, then every minimal zero-sum sequence S of the form S = (g)(n2g)(n3g)(n4g) has index 1. In particular, our result confirms that the above problem has an affirmative answer when the order of G is a product of two different prime numbers or a prime power, extending a recent result by the first author, Plyley, Yuan and Zeng. [ABSTRACT FROM AUTHOR]

Very recently, Frasin [1] introduced and studied the class Hφ(ck, δ) of analytic and univalent functions, where he determined sharp lower bounds for Re{f(z)/fn(z)},Re{fn(z)/f(z)}, Re{f'(z)/fn'(z)} and Re{fn'(z)/f'(z)}.The main object of this paper is to show the upper bounds. [ABSTRACT FROM AUTHOR]

A group G is called morphic if every endomorphism α : G → G for which Gα ⊳ G satisfies G/Gα≅ ker(α). Call an endomorphism α &#x0XCE; end (G) regular if αβα = α for some β &#x0XCE; end (G), and call α unit regular if β can be chosen to be an automorphism of G. The main purpose of this paper is to prove the following group-theoretic analogue of a theorem of Ehrlich: if G is a morphic group, an endomorphism α: G → G for which Gα ⊳ G is unit regular if and only if it is regular. As an application, a cancellation theorem is proved that characterizes the morphic groups among those with regular endomorphism monoids. [ABSTRACT FROM AUTHOR]

A group G is said to be a B(n,k) group if for any n-element subset {a1,..., an} of G, |{aiaj | 1≤i, j≤n}|≤ k. In this paper, characterizations of B(4,11) groups, B(4,12) groups, and B(4,13) non-2-groups are given. [ABSTRACT FROM AUTHOR]

In this paper, strongly Gorenstein flat modules are introduced and investigated. An R-module M is called strongly Gorenstein flat if there is an exact sequence … → P1 → P0 → P0 → P1 → … of projective R-modules with M D ker.P0 ! P1/ such that Hom.??; F/ leaves the sequence exact whenever F is a flat R-module. Several well-known classes of rings are characterized in terms of strongly Gorenstein flat modules. Some examples are given to show that strongly Gorenstein flat modules over coherent rings lie strictly between projective modules and Gorenstein flat modules. The strongly Gorenstein flat dimension and the existence of strongly Gorenstein flat precovers and pre-envelopes are also studied. [ABSTRACT FROM AUTHOR]

Let R be a ring. Recall that a left R-module M is coherent if every finitely generated submodule of M is finitely presented. R is a left coherent ring if the left R-module RR is coherent. In this paper, we say that R is left J-coherent if its Jacobson radical J(R) is a coherent left R-module. J-injective and J-flat modules are introduced to investigate J-coherent rings. Necessary and sufficient conditions for R to be left J-coherent are given. It is shown that there are many similarities between coherent and J-coherent rings. J-injective and J-flat dimensions are also studied. [ABSTRACT FROM AUTHOR]

Let G be a group with cyclic derived subgroup of p-power order (p > 2), and F a field of characteristic p. We determine the derived length of the group of units of the group algebra FG. [ABSTRACT FROM AUTHOR]

Let G be a torsion group and let R be a G-adapted ring. In this note we study the question of when the group ring RG has only trivial torsion units. It turns out that the above question is closely related to the question of when the quaternion group ring RQ8 has only trivial torsion units. We first give a ring-theoretic condition on R which determines exactly when the quaternion group ring has only trivial torsion units. Then several equivalent conditions for RG to have only trivial torsion units are provided. We also investigate the hypercenter of the unit group of a G-adapted group ring RG, and show that when R satisfies the torsion trivial involution condition, this hypercenter is not equal to the center if and only if G is a Q*-group. [ABSTRACT FROM AUTHOR]

Let Z n (??) denote the n'th term of the upper central series of the unit group ?? of Z G and &Ztilde; (??) = Z n (??). It is shown that if the set of torsion elements of G forms a subgroup T and &Ztilde; (??)? C ?? ( T ), then T is either an Abelian 2-group or a Q -group. Moreover, &Ztilde; (??) ? G · C ?? ( T ) whenever G is an FC group. [ABSTRACT FROM AUTHOR]

Nonlinear roll damping has a profound influence on ship motions and stability in ocean waves. In this study, an experimental investigation is conducted on the nonlinear roll damping of a ship in regular and irregular waves. The random decrement method, previously used in linear roll damping prediction, is extended to nonlinear roll damping estimation in the data process. The accuracy of the nonlinear roll damping obtained by using the random decrement method is found to be dependent on the values of the threshold and segment number. [ABSTRACT FROM AUTHOR]