scholarly journals Groups that have the same holomorph as a finite perfect group

2018 ◽  
Vol 507 ◽  
pp. 81-102 ◽  
Author(s):  
A. Caranti ◽  
F. Dalla Volta
Keyword(s):  
Perfect Group

Some Results on Semi-Perfect Group Rings

1974 ◽  
Vol 26 (1) ◽  
pp. 121-129 ◽  
Author(s):  
S. M. Woods
Keyword(s):  
Group Ring ◽  
Polynomial Ring ◽  
Strong Interaction ◽  
Sufficient Conditions ◽  
Group Rings ◽  
Commutative Case ◽  
Perfect Group ◽  
Case Examples ◽  
Complete Answer ◽  
Necessary And Sufficient

The aim of this paper is to find necessary and sufficient conditions on a group G and a ring A for the group ring AG to be semi-perfect. A complete answer is given in the commutative case, in terms of the polynomial ring A[X] (Theorem 5.8). In the general case examples are given which indicate a very strong interaction between the properties of A and those of G. Partial answers to the question are given in Theorem 3.2, Proposition 4.2 and Corollary 4.3.

Restricted Perfect Group Rings

2016 ◽  
Vol 44 (9) ◽  
pp. 4097-4103 ◽  
Author(s):  
Dinesh Udar ◽  
R. K. Sharma ◽  
J. B. Srivastava
Keyword(s):  
Group Rings ◽  
Perfect Group

Perfect Group Photo Synthesis

2015 ◽  
Author(s):  
Chuyang Li ◽  
Rui Qiu ◽  
Kun Li ◽  
Chenlei Lv ◽  
Xin Zheng ◽  
...  
Keyword(s):  
Perfect Group ◽  
Group Photo

scholarly journals W-perfect groups

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Selami Ercan
Keyword(s):  
Present Article ◽  
Perfect Group ◽  
Basic Properties

AbstractIn the present article we define W-paths of elements in a W-perfect group as a useful tools and obtain their basic properties.

scholarly journals FINITELY ANNIHILATED GROUPS

2014 ◽  
Vol 90 (3) ◽  
pp. 404-417 ◽  
Author(s):  
MAURICE CHIODO
Keyword(s):  
Finite Group ◽  
Solvable Group ◽  
Infinite Family ◽  
Finitely Generated ◽  
Perfect Group ◽  
Finitely Generated Groups ◽  
Finitely Presented

AbstractIn 1976, Wiegold asked if every finitely generated perfect group has weight 1. We introduce a new property of groups, finitely annihilated, and show that this might be a possible approach to resolving Wiegold’s problem. For finitely generated groups, we show that in several classes (finite, solvable, free), being finitely annihilated is equivalent to having noncyclic abelianisation. However, we also construct an infinite family of (finitely presented) finitely annihilated groups with cyclic abelianisation. We apply our work to show that the weight of a nonperfect finite group, or a nonperfect finitely generated solvable group, is the same as the weight of its abelianisation. This recovers the known partial results on the Wiegold problem: a finite (or finitely generated solvable) perfect group has weight 1.

On central extensions of algebraic groups

1999 ◽  
Vol 64 (1) ◽  
pp. 68-74 ◽  
Author(s):  
Tuna Altinel ◽  
Gregory Cherlin
Keyword(s):  
Algebraic Group ◽  
Algebraic Groups ◽  
Linear Algebraic Group ◽  
Closed Field ◽  
Morley Rank ◽  
Central Extensions ◽  
Perfect Group ◽  
Theoretic Result ◽  
Abstract Group ◽  
Finite Morley Rank

In this paper the following theorem is proved regarding groups of finite Morley rank which are perfect central extensions of quasisimple algebraic groups.Theorem 1. Let G be a perfect group of finite Morley rank and let C0be a definable central subgroup of G such that G/C0 is a universal linear algebraic group over an algebraically closed field; that is G is a perfect central extension of finite Morley rank of a universal linear algebraic group. Then C0 = 1.Contrary to an impression which exists in some circles, the center of the universal extension of a simple algebraic group, as an abstract group, is not finite in general. Thus the finite Morley rank assumption cannot be omitted.Corollary 1. Let G be a perfect group of finite Morley rank such that G/Z(G) is a quasisimple algebraic group. Then G is an algebraic group. In particular, Z(G) is finite([4], Section 27.5).An understanding of central extensions of quasisimple linear algebraic groups which are groups of finite Morley rank is necessary for the classification of tame simple K*-groups of finite Morley rank, which constitutes an approach to the Cherlin-Zil’ber conjecture. For this reason the theorem above and its corollary were proven in [1] (Theorems 4.1 and 4.2) under the assumption of tameness, which simplifies the argument considerably. The result of the present paper shows that this assumption can be dropped. The main line of argument is parallel to that in [1]; the absence of the tameness assumption will be countered by a model-theoretic result and results from K-theory. The model-theoretic result places limitations on definability in stable fields, and may possibly be relevant to eliminating certain other uses of tameness.

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