The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
The action of Sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their Cayley graphs
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| Creator |
Pawlik, B.T.
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| 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.
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| Date |
2019-06-16T14:38:23Z
2019-06-16T14:38:23Z 2016 |
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| Type |
Article
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| Identifier |
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 |
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| Language |
en
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| Relation |
Algebra and Discrete Mathematics
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| Publisher |
Інститут прикладної математики і механіки НАН України
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