Peyman Niroomand , M. R. R. Moghaddam
Comm. Algebra - , 40, 1188–1193 - March, 2012 - .
Publication year: 2012


Let G be a finite p-group of order p n and ∇(G) be the subgroup of the tensor square of Ggenerated by all symbols x ⊗ x, for all x in G. In the present article, we construct an upper bound for the order of ∇(G) and any extra special p-group. It is also shown that ∇(G) ≅ ∇(G/G′). Using our result, we obtain the explicit structure of the tensor square of Gand π3 SK(G, 1). Finally, the structure of G will be characterized when the bound is attained.