On some series of a group related to the non-abelian tensor square of groups

2021/03/30 by Bastos, Raimundo, de Oliveira, Ricardo, Monetta, Carmine +1 · 1 citation
#20D15 #20F05 #20F14 #20J06 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2103.16366

Abstract

Let G be a group. We denote by ν(G) a certain extension of the non-abelian tensor square G ⊗ G by G × G. In this paper we prove that the derived subgroup ν(G)' is a central product of three normal subgroups of ν(G), all isomorphic to the non-abelian tensor square G ⊗ G. As a consequence, we describe the structure of each term of the derived and lower central series of the group ν(G).

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