Boundedly finite conjugacy classes of tensors

Bastos, Raimundo; Monetta, Carmine

doi:10.22108/ijgt.2020.124368.1643

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	Boundedly finite conjugacy classes of tensors
International Journal of Group Theory
دوره 10، شماره 4، اسفند 2021، صفحه 187-195 اصل مقاله (212.27 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/ijgt.2020.124368.1643
نویسندگان
Raimundo Bastos¹؛ Carmine Monetta^* ²
¹Departamento de Matemática, Universidade de Bras´ ılia, Brasilia-DF Brazil
²Dipartimento di Matematica, Università di Salerno, Salerno, Italy
چکیده
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.
کلیدواژه‌ها
‎structure theorems‎, ‎finiteness conditions؛ non-abelian tensor square of groups

مراجع
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Boundedly finite conjugacy classes of tensors