Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees
A representation of homogeneous symmetric groups by hierarchomorphisms of spherically homogeneous rooted trees are considered. We show that every automorphism of a homogeneous symmetric (alternating) group is locally inner and that the group of all automorphisms contains Cartesian products of arb...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2003 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2003
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/155723 |
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| Zitieren: | Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees / Y.V. Lavrenyuk, V.I. Sushchansky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 4. — С. 33–49. — Бібліогр.: 13 назв. — англ. |
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Lavrenyuk, Y.V. Sushchansky, V.I. 2019-06-17T11:17:16Z 2019-06-17T11:17:16Z 2003 Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees / Y.V. Lavrenyuk, V.I. Sushchansky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 4. — С. 33–49. — Бібліогр.: 13 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 20B35, 20E08, 20F28, 20F50. https://nasplib.isofts.kiev.ua/handle/123456789/155723 A representation of homogeneous symmetric groups by hierarchomorphisms of spherically homogeneous rooted trees are considered. We show that every automorphism of a homogeneous symmetric (alternating) group is locally inner and that the group of all automorphisms contains Cartesian products of arbitrary finite symmetric groups. The structure of orbits on the boundary of the tree where investigated for the homogeneous symmetric group and for its automorphism group. The automorphism group acts highly transitive on the boundary, and the homogeneous symmetric group acts faithfully on every its orbit. All orbits are dense, the actions of the group on different orbits are isomorphic as permutation groups. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees |
| spellingShingle |
Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees Lavrenyuk, Y.V. Sushchansky, V.I. |
| title_short |
Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees |
| title_full |
Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees |
| title_fullStr |
Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees |
| title_full_unstemmed |
Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees |
| title_sort |
automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees |
| author |
Lavrenyuk, Y.V. Sushchansky, V.I. |
| author_facet |
Lavrenyuk, Y.V. Sushchansky, V.I. |
| publishDate |
2003 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| description |
A representation of homogeneous symmetric
groups by hierarchomorphisms of spherically homogeneous rooted
trees are considered. We show that every automorphism of a homogeneous symmetric (alternating) group is locally inner and that
the group of all automorphisms contains Cartesian products of arbitrary finite symmetric groups.
The structure of orbits on the boundary of the tree where investigated for the homogeneous symmetric group and for its automorphism group. The automorphism group acts highly transitive on
the boundary, and the homogeneous symmetric group acts faithfully on every its orbit. All orbits are dense, the actions of the
group on different orbits are isomorphic as permutation groups.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/155723 |
| citation_txt |
Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees / Y.V. Lavrenyuk, V.I. Sushchansky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 4. — С. 33–49. — Бібліогр.: 13 назв. — англ. |
| work_keys_str_mv |
AT lavrenyukyv automorphismsofhomogeneoussymmetricgroupsandhierarchomorphismsofrootedtrees AT sushchanskyvi automorphismsofhomogeneoussymmetricgroupsandhierarchomorphismsofrootedtrees |
| first_indexed |
2025-12-07T19:21:01Z |
| last_indexed |
2025-12-07T19:21:01Z |
| _version_ |
1850878472471183360 |