The homological functors of some finite two-generator two-groups of nilpotency class two

Abstract

The homological functors are originated in homotopy theory. One of the homological functors, namely the nonabelian tensor square, was introduced by Brown and Loday in 1987. Meanwhile, the rest of the homological functors were introduced by Bacon and Kappe in 2003. Some of the homological functors are J (G), �(G), exterior square, the Schur multiplier, �(G), the symmetric square and J�(G). The nonabelian tensor square and some homological functors of some finite two-generator two-groups of nilpotency class two are determined in this research. A software named Groups, Algorithms and Programming (GAP) is used to compute and verify the nonabelian tensor square and some homological functors of some finite two-generator two-groups of nilpotency class two.