Boundedly finite conjugacy classes of tensors

Document Type : Research Paper

Authors

1 Departamento de Matemática, Universidade de Bras´ ılia, Brasilia-DF Brazil

2 Dipartimento di Matematica, Università di Salerno, Salerno, Italy

Abstract

Let $n$ be a positive integer and let $G$ be a group‎. ‎We denote by $\nu(G)$ a certain extension of the non-abelian tensor square $G \otimes G$ by $G \times G$‎. ‎Set $T_{\otimes}(G) = \{g \otimes h \mid g,h \in G\}$‎. ‎We prove that if the size of the conjugacy class $\left |x^{\nu(G)} \right| \leq n$ for every $x \in T_{\otimes}(G)$‎, ‎then the second derived subgroup $\nu(G)''$ is finite with $n$-bounded order‎. ‎Moreover‎, ‎we obtain a sufficient condition for a group to be a BFC-group‎.

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