TY - JOUR ID - 1214 TI - Some numerical results on two classes of finite groups JO - Journal of Algebra and Related Topics JA - JART LA - en SN - 2345-3931 AU - Hashemi, M. AU - Polkouei, M. AD - University of Guilan Y1 - 2015 PY - 2015 VL - 3 IS - 1 SP - 63 EP - 72 KW - Nilpotent groups KW - $n^{th}$-commutativity degree KW - $n$-abelian groups DO - N2 - 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 $g.c.d(s,l)=1$. UR - https://jart.guilan.ac.ir/article_1214.html L1 - https://jart.guilan.ac.ir/article_1214_feb823612fb517d4d22669f4bdc86f76.pdf ER -