The exponent of the non‐abelian tensor square and related constructions of p‐groups. Issue 7 (27th June 2022)

• Record Type: Journal Article
• Authors: Bastos, Raimundo; de Melo, Emerson; Gonçalves, Nathália; Monetta, Carmine
• Is Part Of: Mathematische Nachrichten. Volume 295:Issue 7(2022)
• Page Start: 1264
• Page End: 1278
• Publication Date: 2022-06-27
• Subjects: finite p‐groups -- non‐abelian tensor square of groups; Mathematics -- Periodicals; 510.5
• DOI: 10.1002/mana.202000218
• Languages: English
• ISSNs: 0025-584X

Abstract

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 ) $\nu (G)$ of G ⊗ G $G \otimes G$ by G × G $G \times G$ . In particular, we bound exp ( ν ( G ) ) $\exp (\nu (G))$ in terms of exp ( ν ( G / N ) ) $\exp (\nu (G/N))$ 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.