The exponent of the non‐abelian tensor square and related constructions of <i>p</i> ‐groups

Let $G$ be a finite $p$-group. In this paper we obtain bounds for the exponent of non-abelian tensor square $G \otimes G$ and $\nu(G)$, which is certain extension by \times G$. particular, bound $\exp(\nu(G))$ in terms $\exp(\nu(G/N))$ $\exp(N)$ when admits some specific normal subgroup $N$. We also establish $\exp(G G)$ $\exp(G)$ either nilpotency class or coclass group $G$, improving existing bounds.