Computing the nonabelian tensor squares of groups of order $$\pmb {p^3q}$$

Abstract In this paper, we describe the explicit structures of nonabelian tensor squares groups order $$p^3q$$ p 3 q , where p and q are distinct prime numbers $$p>2$$ > 2 . Our method is based on determining their Schur multipliers by applying some well-known results presentations groups, which leads us to obtain orders squares.