Non-abelian tensor square and related constructions of p-groups

2019/06/18 by Bastos, Raimundo, de Melo, Emerson, Gonçalves, Nathália +1 · 1 citation
#20D15 #20E06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1906.07830

Abstract

Let G be a group. We denote by ν(G) a certain extension of the non-abelian tensor square [G,G^φ] by G × G. We prove that if G is a finite potent p-group, then [G,G^φ] and the k-th term of the lower central series γ_k(ν(G)) are potently embedded in ν(G) (Theorem A). Moreover, we show that if G is a potent p-group, then the exponent exp(ν(G)) divides p ⋅ exp(G) (Theorem B). We also study the weak commutativity construction of powerful p-groups (Theorem C).

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