ABSTRACT

Let G be a finite non-abelian simple group and d(G) the minimum number of generators of G. Then, h(2,G) is the maximum number n such that d(Gn) = 2, where Gn is the external direct products of n copies of ...

Let $G$ be a finitely generated group and $G^n$ be the direct

product of $n$ copies of $G$. The growth sequence of $G$ is the

sequence $\\\\\\\\\\\\\\\\{d(G^n)\\\\\\\\\\\\\\\\}_{n \\\\\\\\\\\\\\\\geq1}$, where ...

Following [1] and [5], if Gis a finite group, the probability

that two randomly chosen elements of Gcommute is defined to becom(G)/|G|^2, where com(G) is the number of pairs

(x,y)in G times G$ with xy=yx For ...

A pair ( varphi,psi) is called an isoclinism between groups G

and H if varphi is an isomorphism from G/Z(G) to H/Z(H),

psi is also an isomorphism from G to H and psi

([g_1,g_2])=[h_1,h_2]whenever h_i ...

In this talk, we will give a brief survey of some aspects in the

probability group theory. We will also focus on two old problems

given by Erdos and Turan [1] on random generating set for a given

group ...

Let G be a group, then G is said to be a tidy group if for every

element xin G, the set {yin Gla x,yrambox{ is cyclic}}

is a subgroup of G. The aim of this paper is to investigate the

above property ...

A pair ('; ) is called an isoclinism between groups G and H if '

is an isomorphism from G=Z(G) to H=Z(H), is also an isomorphism

from G0 to H0 and ([g1; g2]) = [h1; h2] whenever hi 2 '(giZ(G)), for

all ...