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| \le...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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University of Isfahan
2021-12-01
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| Series: | International Journal of Group Theory |
| Subjects: | |
| Online Access: | https://ijgt.ui.ac.ir/article_25060_2f6d29096899cad81af9341e68a868aa.pdf |
| _version_ | 1819105207910400000 |
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| author | Raimundo Bastos Carmine Monetta |
| author_facet | Raimundo Bastos Carmine Monetta |
| author_sort | Raimundo Bastos |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-22T02:18:35Z |
| format | Article |
| id | doaj.art-1ee5614747af4f14b40261809ff36213 |
| institution | Directory Open Access Journal |
| issn | 2251-7650 2251-7669 |
| language | English |
| last_indexed | 2024-12-22T02:18:35Z |
| publishDate | 2021-12-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | International Journal of Group Theory |
| spelling | doaj.art-1ee5614747af4f14b40261809ff362132022-12-21T18:42:11ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692021-12-0110418719510.22108/ijgt.2020.124368.164325060Boundedly finite conjugacy classes of tensorsRaimundo Bastos0Carmine Monetta1Departamento de Matemática, Universidade de Bras´ ılia, Brasilia-DF BrazilDipartimento di Matematica, Università di Salerno, Salerno, ItalyLet $n$ 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.https://ijgt.ui.ac.ir/article_25060_2f6d29096899cad81af9341e68a868aa.pdfstructure theorems, finiteness conditionsnon-abelian tensor square of groups |
| spellingShingle | Raimundo Bastos Carmine Monetta Boundedly finite conjugacy classes of tensors International Journal of Group Theory structure theorems, finiteness conditions non-abelian tensor square of groups |
| title | Boundedly finite conjugacy classes of tensors |
| title_full | Boundedly finite conjugacy classes of tensors |
| title_fullStr | Boundedly finite conjugacy classes of tensors |
| title_full_unstemmed | Boundedly finite conjugacy classes of tensors |
| title_short | Boundedly finite conjugacy classes of tensors |
| title_sort | boundedly finite conjugacy classes of tensors |
| topic | structure theorems, finiteness conditions non-abelian tensor square of groups |
| url | https://ijgt.ui.ac.ir/article_25060_2f6d29096899cad81af9341e68a868aa.pdf |
| work_keys_str_mv | AT raimundobastos boundedlyfiniteconjugacyclassesoftensors AT carminemonetta boundedlyfiniteconjugacyclassesoftensors |