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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 S₂n 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 Pn(2) of S₂n acts by conjugation on the set of all bases. In presented pap...
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Інститут прикладної математики і механіки НАН України
2016
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| Series: | Algebra and Discrete Mathematics |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/155248 |
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irk-123456789-1552482019-06-17T01:28:25Z The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs Pawlik, B.T. Base (minimal generating set) of the Sylow 2-subgroup of S₂n 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 Pn(2) of S₂n acts by conjugation on the set of all bases. In presented paper the~stabilizer of the set of all diagonal bases in Sn(2) is characterized and the orbits of the action are determined. It is shown that every orbit contains exactly 2n−1 diagonal bases and 2²n−²n bases at all. Recursive construction of Cayley graphs of Pn(2) on diagonal bases (n≥2) is proposed. 2016 Article The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs / B.T. Pawlik // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 264–281. — Бібліогр.: 6 назв. — англ. 1726-3255 2010 MSC:20B35, 20D20, 20E22, 05C25. http://dspace.nbuv.gov.ua/handle/123456789/155248 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
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English |
| description |
Base (minimal generating set) of the Sylow 2-subgroup of S₂n 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 Pn(2) of S₂n acts by conjugation on the set of all bases. In presented paper the~stabilizer of the set of all diagonal bases in Sn(2) is characterized and the orbits of the action are determined. It is shown that every orbit contains exactly 2n−1 diagonal bases and 2²n−²n bases at all. Recursive construction of Cayley graphs of Pn(2) on diagonal bases (n≥2) is proposed. |
| format |
Article |
| author |
Pawlik, B.T. |
| spellingShingle |
Pawlik, B.T. The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs Algebra and Discrete Mathematics |
| author_facet |
Pawlik, B.T. |
| author_sort |
Pawlik, B.T. |
| 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 |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/155248 |
| citation_txt |
The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs / B.T. Pawlik // Algebra and Discrete Mathematics. — 2016. — Vol. 21, № 2. — С. 264–281. — Бібліогр.: 6 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
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| first_indexed |
2023-05-20T17:46:26Z |
| last_indexed |
2023-05-20T17:46:26Z |
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1796154060366151680 |