%0 Journal Article
%T Some numerical results on two classes of finite groups
%J Journal of Algebra and Related Topics
%I University of Guilan
%Z 2345-3931
%A Hashemi, M.
%A Polkouei, M.
%D 2015
%\ 06/01/2015
%V 3
%N 1
%P 63-72
%! Some numerical results on two classes of finite groups
%K Nilpotent groups
%K $n^{th}$-commutativity degree
%K $n$-abelian groups
%R
%X In this paper, we consider the finitely presented groups $G_{m}$ and $K(s,l)$ as follows;$$G_{m}=langle a,b| a^m=b^m=1,~[a,b]^a=[a,b],~[a,b]^b=[a,b]rangle $$$$K(s,l)=langle a,b|ab^s=b^la,~ba^s=a^lbrangle;$$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, $m,ngeq 2$ and $g.c.d(s,l)=1$.
%U https://jart.guilan.ac.ir/article_1214_feb823612fb517d4d22669f4bdc86f76.pdf