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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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