Conjugacy and order classes of two-generator p-groups of nilpotency class two

Abstract

For nilpotent groups, researchers only estimate the number of conjugacy classes by giving the lower bound of these groups. The difficulty of providing a formula for the exact number of conjugacy classes of these groups is because the structure of these groups are not easily understood. In this thesis, 2-generator p-groups of nilpotency class 2 (p an odd prime) are considered. These groups were classified by Bacon and Kappe in 1993 and Kappe, Sarmin and Visscher did a minor correction in 1999.