Some applications of Two-Generator p-Groups of Nilpotency class two

Abstract

The classification of all two-generator groups of nilpotency class two have been done by Nor Haniza Sarmin in 2000. Earlier research on the finite case was introduced by Kappe et. al in 1999 and Bacon and Kappe in 1993. Later, in 2000, James Beuerle and Kappe focus their classification to infinite metacyclic groups and some of their applications. This paper will focus on the applications of two-generator p-groups of nilpotency class two including the nonabelian tensor squares and the exterior squares. We will also determine which of these groups are capable.