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 (Citation1973) and Moghaddam et al. (Citation2005). 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.
2000 Mathematics Subject Classification:
ACKNOWLEDGMENTS
The first and the second authors thank the Centre of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad for supporting the part grant on this work. Moreover, the third author also wishes to thank the Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette) for its hospitality in October and November 2005, at which time part of the work on this article was done.
Notes
Communicated by J. Alev.