Boundedly finite conjugacy classes of tensors

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.

کلیدواژه ها:

‎structure theorems‎ ، ‎finiteness conditions ، Non-abelian tensor square of groups