Some numerical results on two classes of finite groups

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=۱,~[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 ۲ and g.c.d(s,l)=۱.

Keywords:

Nilpotent groups , n^{th}-commutativity degree , n-abelian groups