The exponent of the non‐abelian tensor square and related constructions of p‐groups. Issue 7 (27th June 2022) - Bastos, Raimundo; de Melo, Emerson; Gonçalves, Nathália; Monetta, Carmine
Abstract: Let G be a finite p ‐group. In this paper we obtain bounds for the exponent of the non‐abelian tensor square G ⊗ G $G \otimes G$ and a certain extension ν ( G ) $ν (G)$ of G ⊗ G $G \otimes G$ by G × G $G × G$ . In particular, we bound exp ( ν ( G ) ) $\exp (ν (G))$ in terms of exp ( ν ( G / N ) ) $\exp (ν (G/N))$ and exp ( N ) $\exp (N)$ when G admits some specific normal subgroup N . We also establish bounds for exp ( G ⊗ G ) $\exp (G \otimes G)$ in terms of exp ( G ) $\exp (G)$ and either the nilpotency class or the coclass of the group G, improving some existing bounds.