Minimal generating sets and Cayley graphs of Sylow \(p\)-subgroups of finite symmetric groups
Minimal generating sets of a Sylow \(p\)-subgroup \(P_n\) of the symmetric group \(S_{p^n}\) are characterized. The number of ordered minimal generating sets of \(P_n\) is calculated. The notion of the type of a generating set of \(P_n\) is introduced and it is proved that \(P_n\) contains minimal g...
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| Date: | 2018 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/803 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543317923201024 |
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| author | Slupik, Anna J. Sushchansky, Vitaly I. |
| author_facet | Slupik, Anna J. Sushchansky, Vitaly I. |
| author_sort | Slupik, Anna J. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-04T08:49:22Z |
| description | Minimal generating sets of a Sylow \(p\)-subgroup \(P_n\) of the symmetric group \(S_{p^n}\) are characterized. The number of ordered minimal generating sets of \(P_n\) is calculated. The notion of the type of a generating set of \(P_n\) is introduced and it is proved that \(P_n\) contains minimal generating sets of all possible type. The isomorphism problem of Cayley graphs of \(P_n\) with respect to their minimal generating sets is discussed. |
| first_indexed | 2025-12-02T15:27:59Z |
| format | Article |
| id | admjournalluguniveduua-article-803 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:27:59Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-8032018-04-04T08:49:22Z Minimal generating sets and Cayley graphs of Sylow \(p\)-subgroups of finite symmetric groups Slupik, Anna J. Sushchansky, Vitaly I. Cayley graph, Sylow \(p\)-subgroup, Frattini subgroup 20B35, 05C25, 05C12, 20F65 Minimal generating sets of a Sylow \(p\)-subgroup \(P_n\) of the symmetric group \(S_{p^n}\) are characterized. The number of ordered minimal generating sets of \(P_n\) is calculated. The notion of the type of a generating set of \(P_n\) is introduced and it is proved that \(P_n\) contains minimal generating sets of all possible type. The isomorphism problem of Cayley graphs of \(P_n\) with respect to their minimal generating sets is discussed. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/803 Algebra and Discrete Mathematics; Vol 8, No 4 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/803/333 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | Cayley graph Sylow \(p\)-subgroup Frattini subgroup 20B35 05C25 05C12 20F65 Slupik, Anna J. Sushchansky, Vitaly I. Minimal generating sets and Cayley graphs of Sylow \(p\)-subgroups of finite symmetric groups |
| title | Minimal generating sets and Cayley graphs of Sylow \(p\)-subgroups of finite symmetric groups |
| title_full | Minimal generating sets and Cayley graphs of Sylow \(p\)-subgroups of finite symmetric groups |
| title_fullStr | Minimal generating sets and Cayley graphs of Sylow \(p\)-subgroups of finite symmetric groups |
| title_full_unstemmed | Minimal generating sets and Cayley graphs of Sylow \(p\)-subgroups of finite symmetric groups |
| title_short | Minimal generating sets and Cayley graphs of Sylow \(p\)-subgroups of finite symmetric groups |
| title_sort | minimal generating sets and cayley graphs of sylow \(p\)-subgroups of finite symmetric groups |
| topic | Cayley graph Sylow \(p\)-subgroup Frattini subgroup 20B35 05C25 05C12 20F65 |
| topic_facet | Cayley graph Sylow \(p\)-subgroup Frattini subgroup 20B35 05C25 05C12 20F65 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/803 |
| work_keys_str_mv | AT slupikannaj minimalgeneratingsetsandcayleygraphsofsylowpsubgroupsoffinitesymmetricgroups AT sushchanskyvitalyi minimalgeneratingsetsandcayleygraphsofsylowpsubgroupsoffinitesymmetricgroups |