Automorphisms of direct products of finite groups

2006 ◽  
Vol 86 (6) ◽  
pp. 481-489 ◽  
Author(s):  
J. N. S. Bidwell ◽  
M. J. Curran ◽  
D. J. McCaughan
Keyword(s):  
Finite Groups ◽  
Direct Products

scholarly journals Direct products of finite groups as unions of proper subgroups

2010 ◽  
Vol 95 (3) ◽  
pp. 201-206 ◽  
Author(s):  
Martino Garonzi ◽  
Andrea Lucchini
Keyword(s):  
Finite Groups ◽  
Direct Products

Automorphisms of direct products of finite groups II

2008 ◽  
Vol 91 (2) ◽  
pp. 111-121 ◽  
Author(s):  
J. N. S. Bidwell
Keyword(s):  
Finite Groups ◽  
Direct Products

scholarly journals CONJUGACY CLASS SIZES OF CERTAIN DIRECT PRODUCTS

2012 ◽  
Vol 85 (2) ◽  
pp. 217-231
Author(s):  
CARLO CASOLO ◽  
ELISA MARIA TOMBARI
Keyword(s):  
Conjugacy Class ◽  
Finite Groups ◽  
Prime Divisor ◽  
Full Description ◽  
Direct Products ◽  
Conjugacy Class Sizes

AbstractWe consider finite groups in which, for all primes p, the p-part of the length of any conjugacy class is trivial or fixed. We obtain a full description in the case in which for each prime divisor p of the order of the group there exists a noncentral conjugacy class of p-power size.

scholarly journals Proficient presentations and direct products of finite groups

1999 ◽  
Vol 60 (2) ◽  
pp. 177-189 ◽  
Author(s):  
K.W. Gruenberg ◽  
L.G. Kovács
Keyword(s):  
Finite Group ◽  
Normal Subgroup ◽  
Free Group ◽  
Finite Groups ◽  
Finite Rank ◽  
Module Structure ◽  
Direct Products ◽  
The Difference ◽  
A Finite Group ◽  
Open Question

Let G be a finite group, F a free group of finite rank, R the kernel of a homomorphism φ of F onto G, and let [R, F], [R, R] denote mutual commutator subgroups. Conjugation in F yields a G-module structure on R/[R, R] let dg(R/[R, R]) be the number of elements required to generate this module. Define d(R/[R, F]) similarly. By an earlier result of the first author, for a fixed G, the difference dG(R/[R, R]) − d(R/[R, F]) is independent of the choice of F and φ; here it is called the proficiency gap of G. If this gap is 0, then G is said to be proficient. It has been more usual to consider dF(R), the number of elements required to generate R as normal subgroup of F: the group G has been called efficient if F and φ can be chosen so that dF(R) = dG(R/[R, F]). An efficient group is necessarily proficient; but (though usually expressed in different terms) the converse has been an open question for some time.

Direct products of inseparable finite groups, II

1997 ◽  
Vol 25 (1) ◽  
pp. 243-246 ◽  
Author(s):  
Joseph Kirtland
Keyword(s):  
Finite Groups ◽  
Direct Products

scholarly journals AUTOMORPHISM CRITERIA FOR M*-GROUPS

2004 ◽  
Vol 47 (2) ◽  
pp. 339-351 ◽  
Author(s):  
Emilio Bujalance ◽  
Francisco-Javier Cirre ◽  
Peter Turbek
Keyword(s):  
Finite Groups ◽  
Commutator Subgroup ◽  
Subject Classification ◽  
Direct Products ◽  
Primary 20D45

AbstractWe prove that the determination of all $M^*$-groups is essentially equivalent to the determination of finite groups generated by an element of order 3 and an element of order 2 or 3 that admit a particular automorphism. We also show how the second commutator subgroup of an $M^*$-group $G$ can often be used to construct $M^*$-groups which are direct products with $G$ as one factor. Several applications of both methods are given.AMS 2000 Mathematics subject classification: Primary 20D45; 20E36. Secondary 14H37; 30F50

scholarly journals ZL-amenability and characters for the restricted direct products of finite groups

2014 ◽  
Vol 411 (1) ◽  
pp. 314-328 ◽  
Author(s):  
Mahmood Alaghmandan ◽  
Yemon Choi ◽  
Ebrahim Samei
Keyword(s):  
Finite Groups ◽  
Direct Products
Sign in / Sign up

Export Citation Format

Share Document