The probability that two elements commute in some 2-generator 2-groups of nilpotency class 2

Abstract

Erdos and Turan have introduced the determination of the abelianness of a finite group for symmetric groups, finite groups and finite rings in 1968. Basic probability theory will be used in studying its connection with group theory. Some basic concepts related with P(G) , the probability a random pair of elements in a group commutes, will be presented. This research will focus on the 2-generator 2- groups of nilpotency class 2, based on the classification that have been done by Kappe et.al in 1999. Finally, some properties of P(G) for some 2-generator 2- groups of nilpotency class 2 will be determined