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...
Saved in:
| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2016 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2016
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155248 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862725977300271104 |
|---|---|
| author | Pawlik, B.T. |
| author_facet | Pawlik, B.T. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T18:55:30Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155248 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T18:55:30Z |
| publishDate | 2016 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| 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 | 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_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_sort | action of sylow 2-subgroups of symmetric groups on the set of bases and the problem of isomorphism of their cayley graphs |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155248 |
| work_keys_str_mv | AT pawlikbt theactionofsylow2subgroupsofsymmetricgroupsonthesetofbasesandtheproblemofisomorphismoftheircayleygraphs AT pawlikbt actionofsylow2subgroupsofsymmetricgroupsonthesetofbasesandtheproblemofisomorphismoftheircayleygraphs |