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 ...