Some numerical results on two classes of finite groups

Document Type: Research Paper

Authors

University of Guilan

Abstract

In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;
$$G_{m}=\langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]\rangle $$
$$K(s,l)=\langle a,b|ab^s=b^la,~ba^s=a^lb\rangle;$$
and find the $n^{th}$-commutativity degree for each of them. Also we study the concept of $n$-abelianity on these groups, where $m,n,s$ and $l$ are positive integers, $m,n\geq 2$ and $g.c.d(s,l)=1$.

Keywords