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).

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

Monetta C.;
2022

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4806800
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