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.;
2022-01-01
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).File in questo prodotto:
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