A BOUND ON THE ORDER OF NON-ABELIAN TENSOR SQUARE OF A PRIME-POWER GROUP

This article improves on an upper bound for the order of the non-abelian tensor square of a finite p-group G given in [3]. In particular, applying this for finite p-groups of order p(n) with factor group G/G' of order p(m), the bound p(nm) attains if and only if G is elementary abelian of rank n, quaternion group of order 8, or extra special p-group of order p(3) with odd exponent p.