On The Exterior Degree of Some Finite p-Groups

Abstract

In any finite group G, the commutativity degree of G (denoted by P(G)) is the probability that two randomly chosen elements of G commute. P(G) has been introduced by Erdos and Turan (1968) for symmetric groups. Gustafson (1973) did the same for compact groups while MacHale (1974) determined the commutativity degree of finite rings. The exterior square of G, denoted as G ˄ G, is defined as G ˄ G = G7G/d(G) where (G7G) is the nonabelian tensor square of G and d(G) is a subgroup of G generated by x7x for all xdG. Recently, Niroomand and Rezaei (2011) give some relations between the concept of exterior square and commutativity degree by defining the exterior degree of a finite group G, denoted as P/(G), to be the probability for two elements g and g' in G such that g / g' = 1 where 1/, is the identity of G/G. In this paper, the exterior degree of some finite groups is presented.