On the Relative Commutativity Degree of a Subgroup of a Finite Group

Abstract

The aim of this article is to give a generalization of the concept of commutativity degree of a finite group G (denoted by d(G)), to the concept of relative commutativity degree of a subgroup H of a group G (denoted by d(H, G)). We shall state some results concerning the new concept which are mostly new or improvements of known results given in Gustafson (1973 Gustafson , W. H. ( 1973 ). What is the probability that two group elements commute? Amer. Math. Monthly 80 : 1031 – 1304 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) and Moghaddam et al. (2005 Moghaddam , M. R. R. , Chiti , K. , Salemkar , A. R. ( 2005 ). n-Isoclinism classes and n-nilpotency degree of finite groups . Algebra Colloquium 12 ( 2 ): 225 – 261 .[Crossref], [Web of Science ®] , [Google Scholar]). Moreover, we shall define the relative nth nilpotency degree of a subgroup of a group and give some results concerning this at the end of the article.