The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs
Base (minimal generating set) of the Sylow 2-subgroup of \(S_{2^n}\) is called diagonal if every element of this set acts non-trivially only on one coordinate, and different elements act on different coordinates. The Sylow 2-subgroup \(P_n(2)\) of \(S_{2^n}\) acts by conjugation on the set of all b...
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| Date: | 2016 |
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| Language: | English |
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Lugansk National Taras Shevchenko University
2016
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| Journal Title: | Algebra and Discrete Mathematics |
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admjournalluguniveduua-article-2332016-07-12T10:09:40Z The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs Pawlik, Bartłomiej Tadeusz Sylow \(p\)-subgroup, group base, wreath product of groups, Cayley graphs 20B35, 20D20, 20E22, 05C25 Base (minimal generating set) of the Sylow 2-subgroup of \(S_{2^n}\) is called diagonal if every element of this set acts non-trivially only on one coordinate, and different elements act on different coordinates. The Sylow 2-subgroup \(P_n(2)\) of \(S_{2^n}\) acts by conjugation on the set of all bases. In presented paper the~stabilizer of the set of all diagonal bases in \(S_n(2)\) is characterized and the orbits of the action are determined. It is shown that every orbit contains exactly \(2^{n-1}\) diagonal bases and \(2^{2^n-2n}\) bases at all. Recursive construction of Cayley graphs of \(P_n(2)\) on diagonal bases (\(n\geq2\)) is proposed. Lugansk National Taras Shevchenko University 2016-07-12 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/233 Algebra and Discrete Mathematics; Vol 21, No 2 (2016) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/233/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/233/92 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/233/93 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/233/94 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/233/95 Copyright (c) 2016 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
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| datestamp_date |
2016-07-12T10:09:40Z |
| collection |
OJS |
| language |
English |
| topic |
Sylow \(p\)-subgroup group base wreath product of groups Cayley graphs 20B35 20D20 20E22 05C25 |
| spellingShingle |
Sylow \(p\)-subgroup group base wreath product of groups Cayley graphs 20B35 20D20 20E22 05C25 Pawlik, Bartłomiej Tadeusz The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs |
| topic_facet |
Sylow \(p\)-subgroup group base wreath product of groups Cayley graphs 20B35 20D20 20E22 05C25 |
| format |
Article |
| author |
Pawlik, Bartłomiej Tadeusz |
| author_facet |
Pawlik, Bartłomiej Tadeusz |
| author_sort |
Pawlik, Bartłomiej Tadeusz |
| title |
The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs |
| title_short |
The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs |
| title_full |
The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs |
| title_fullStr |
The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs |
| title_full_unstemmed |
The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs |
| title_sort |
action of sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their cayley graphs |
| description |
Base (minimal generating set) of the Sylow 2-subgroup of \(S_{2^n}\) is called diagonal if every element of this set acts non-trivially only on one coordinate, and different elements act on different coordinates. The Sylow 2-subgroup \(P_n(2)\) of \(S_{2^n}\) acts by conjugation on the set of all bases. In presented paper the~stabilizer of the set of all diagonal bases in \(S_n(2)\) is characterized and the orbits of the action are determined. It is shown that every orbit contains exactly \(2^{n-1}\) diagonal bases and \(2^{2^n-2n}\) bases at all. Recursive construction of Cayley graphs of \(P_n(2)\) on diagonal bases (\(n\geq2\)) is proposed. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2016 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/233 |
| work_keys_str_mv |
AT pawlikbartłomiejtadeusz theactionofsylow2subgroupsofsymmetricgroupsonthesetofbasesandtheproblemofisomorphismoftheircayleygraphs AT pawlikbartłomiejtadeusz actionofsylow2subgroupsofsymmetricgroupsonthesetofbasesandtheproblemofisomorphismoftheircayleygraphs |
| first_indexed |
2025-12-02T15:42:39Z |
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2025-12-02T15:42:39Z |
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1850411749212160000 |