The Schur multiplier and nonabelian tensor square of some groups of p-power order

Abstract

Let G be a group. The Schur multiplier of the group, M(G), is the second homology group of G with integer coefficients. In 1987, the nonabelian tensor square, G ⊗ G, of a group G was introduced. Nonabelian tensor square is one of the homological invariant which originated in homotopy theory. In this research, we determine the Schur multiplier and nonabelian tensor square of groups of order p3 and p4, where p is an odd prime.