On products of conjugacy classes in general linear groups
Let $K$ be a field and $n\geq 3$. Let $E_n(K)\leq H\leq GL_n(K)$ be an intermediate group and $C$ a noncentral $H$-class. Define $m(C)$ as the minimal positive integer $m$ such that $\exists i_1,\ldots,i_m\in\{\pm 1\}$ such that the product $C^{i_1}\cdots C^{i_m}$ contains all nontrivial elementary...
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| Format: | Article |
| Language: | English |
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University of Isfahan
2022-12-01
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| Series: | International Journal of Group Theory |
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| Online Access: | https://ijgt.ui.ac.ir/article_26036_36aaaeb1e50575a14d9de67d71f69ab6.pdf |
| _version_ | 1797988560878436352 |
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| author | Raimund Preusser |
| author_facet | Raimund Preusser |
| author_sort | Raimund Preusser |
| collection | DOAJ |
| description | Let $K$ be a field and $n\geq 3$. Let $E_n(K)\leq H\leq GL_n(K)$ be an intermediate group and $C$ a noncentral $H$-class. Define $m(C)$ as the minimal positive integer $m$ such that $\exists i_1,\ldots,i_m\in\{\pm 1\}$ such that the product $C^{i_1}\cdots C^{i_m}$ contains all nontrivial elementary transvections. In this article we obtain a sharp upper bound for $m(C)$. Moreover, we determine $m(C)$ for any noncentral $H$-class $C$ under the assumption that $K$ is algebraically closed or $n=3$ or $n=\infty$. |
| first_indexed | 2024-04-11T08:05:58Z |
| format | Article |
| id | doaj.art-72b10a25d45a4cb58f2b24b25e9f7f37 |
| institution | Directory Open Access Journal |
| issn | 2251-7650 2251-7669 |
| language | English |
| last_indexed | 2024-04-11T08:05:58Z |
| publishDate | 2022-12-01 |
| publisher | University of Isfahan |
| record_format | Article |
| series | International Journal of Group Theory |
| spelling | doaj.art-72b10a25d45a4cb58f2b24b25e9f7f372022-12-22T04:35:34ZengUniversity of IsfahanInternational Journal of Group Theory2251-76502251-76692022-12-0111422925210.22108/ijgt.2021.123469.162726036On products of conjugacy classes in general linear groupsRaimund Preusser0Chebyshev Laboratory, St. Petersburg State University, RussiaLet $K$ be a field and $n\geq 3$. Let $E_n(K)\leq H\leq GL_n(K)$ be an intermediate group and $C$ a noncentral $H$-class. Define $m(C)$ as the minimal positive integer $m$ such that $\exists i_1,\ldots,i_m\in\{\pm 1\}$ such that the product $C^{i_1}\cdots C^{i_m}$ contains all nontrivial elementary transvections. In this article we obtain a sharp upper bound for $m(C)$. Moreover, we determine $m(C)$ for any noncentral $H$-class $C$ under the assumption that $K$ is algebraically closed or $n=3$ or $n=\infty$.https://ijgt.ui.ac.ir/article_26036_36aaaeb1e50575a14d9de67d71f69ab6.pdfgeneral linear groupsconjugacy classesmatrix identities |
| spellingShingle | Raimund Preusser On products of conjugacy classes in general linear groups International Journal of Group Theory general linear groups conjugacy classes matrix identities |
| title | On products of conjugacy classes in general linear groups |
| title_full | On products of conjugacy classes in general linear groups |
| title_fullStr | On products of conjugacy classes in general linear groups |
| title_full_unstemmed | On products of conjugacy classes in general linear groups |
| title_short | On products of conjugacy classes in general linear groups |
| title_sort | on products of conjugacy classes in general linear groups |
| topic | general linear groups conjugacy classes matrix identities |
| url | https://ijgt.ui.ac.ir/article_26036_36aaaeb1e50575a14d9de67d71f69ab6.pdf |
| work_keys_str_mv | AT raimundpreusser onproductsofconjugacyclassesingenerallineargroups |