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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155248 |
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| Zitieren: | 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. |
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Pawlik, B.T. 2019-06-16T14:38:23Z 2019-06-16T14:38:23Z 2016 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. https://nasplib.isofts.kiev.ua/handle/123456789/155248 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs |
| spellingShingle |
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. |
| 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 |
| author |
Pawlik, B.T. |
| author_facet |
Pawlik, B.T. |
| publishDate |
2016 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.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. |
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2025-12-07T18:55:30Z |
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