scholarly journals On the number of generators needed for free profinite products of finite groups

2007 ◽  
Vol 162 (1) ◽  
pp. 81-92
Author(s):  
Miklós Abért ◽  
Pál Hegedűs
Keyword(s):  
Finite Groups ◽  
Number Of Generators

MINIMAL NUMBER OF GENERATORS AND COMPOSITION LENGTH OF SOCLE IN FINITE GROUPS

1996 ◽  
Vol 47 (2) ◽  
pp. 157-163 ◽  
Author(s):  
FRANCESCA DALLA VOLTA ◽  
ANDREA LUCCHINI
Keyword(s):  
Finite Groups ◽  
Number Of Generators

Some finite groups with zero deficiency

1974 ◽  
Vol 18 (1) ◽  
pp. 73-75 ◽  
Author(s):  
J. W. Wamsley
Keyword(s):  
Finite Groups ◽  
Generators And Relations ◽  
Number Of Generators

AbstractWe introduce further finite groups which can be presented with an equal number of generators and relations.

Inequalities for Baer Invariants of Finite Groups

1998 ◽  
Vol 41 (4) ◽  
pp. 385-391 ◽  
Author(s):  
John Burns ◽  
Graham Ellis
Keyword(s):  
Exact Sequence ◽  
Finite Groups ◽  
Generating Sets ◽  
Number Of Generators ◽  
Explicit Bound

AbstractIn this note we further our investigation of Baer invariants of groups by obtaining, as consequences of an exact sequence of A. S.-T. Lue, some numerical inequalities for their orders, exponents, and generating sets. An interesting group theoretic corollary is an explicit bound for |γc+1 (G)| given that G, Zc(G) is a finite p-group with prescribed order and number of generators.

scholarly journals On a class of finite groups

1975 ◽  
Vol 19 (3) ◽  
pp. 290-291
Author(s):  
J. W. Wamsley
Keyword(s):  
Finite Groups ◽  
Normal Closure ◽  
Number Of Generators ◽  
Image Position

Let G be a finite P-group. Denote dim H1 (G, Zp) by d(G) and dimH2(G, Zp) by r(G), then d(G) is the minimal number of generators of G and G has a presentation where F is free on x1, …, xd(G) and R is the normal closure in F of R1, …, Rm. We have always that m ≧ r(G) = d(R/[F, R]) and we say that G belongs to a class, Gp, of the finite pgroups if m = r(G). It is well known (see for example Johnson and Wamsley (1970)) that if G and H are finite p-groups then r(G x H) = r(G) + r(H) + d(G)d(H) and hence G, H∈Gp implies Gx H∈Gp, also it is shown in Wamsley (1972) that if G is any finite pgroup then there exists an H∈Gp such that G x H belongs to Gp. Let G1 = G and Gk = Gk-1 x G then we show in this note that if G is any finite p-group, there exists an integer n(G), such that Gk∈Gp for alal k ≧ n(G).

scholarly journals Growth sequences of finite groups V

1981 ◽  
Vol 31 (3) ◽  
pp. 374-375 ◽  
Author(s):  
D. Meier ◽  
James Wiegold
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Finite Groups ◽  
The Other ◽  
Direct Power ◽  
Easy Proof ◽  
Number Of Generators ◽  
Other Hand ◽  
Minimum Number

AbstractA short and easy proof that the minimum number of generators of the nth direct power of a non-trival finite group of order s having automorphism group of order a is more than logsn + logsa, n > 1. On the other hand, for non-abelian simple G and large n, d(Gn) is within 1 + e of logsn + logsa.

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