scholarly journals On a problem of M. P. Schützenberger

1980 ◽  
Vol 23 (3) ◽  
pp. 243-247 ◽  
Author(s):  
D. B. McAlister
Keyword(s):  
Finite Groups ◽  
Direct Products ◽  
Finite Semigroups ◽  
The University

A class of finite semigroups is called a genus if it is closed under homomorphic images, subsemigroups and finite direct products. During a talk at the Symposium on Semigroups held at the University of St Andrews, in 1976, M. P. Schützenberger posed the problem of characterising the smallest genus which contains finite groups and finite semigroups, all of whose subgroups are trivial.

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

PROFINITE IDENTITIES FOR FINITE SEMIGROUPS WHOSE SUBGROUPS BELONG TO A GIVEN PSEUDOVARIETY

2003 ◽  
Vol 02 (02) ◽  
pp. 137-163 ◽  
Author(s):  
J. ALMEIDA ◽  
M. V. VOLKOV
Keyword(s):  
Finite Groups ◽  
Finitely Based ◽  
Finite Semigroups

We introduce a series of new polynomially computable implicit operations on the class of all finite semigroups. These new operations enable us to construct a finite pro-identity basis for the pseudovariety [Formula: see text] of all finite semigroups whose subgroups belong to a given finitely based pseudovariety H of finite groups.

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