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 C...
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| Published in: | Algebra and Discrete Mathematics |
|---|---|
| Date: | 2003 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут прикладної математики і механіки НАН України
2003
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/155723 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862730567618920448 |
|---|---|
| author | Lavrenyuk, Y.V. Sushchansky, V.I. |
| author_facet | Lavrenyuk, Y.V. Sushchansky, V.I. |
| 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. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
|
| first_indexed | 2025-12-07T19:21:01Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-155723 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-12-07T19:21:01Z |
| publishDate | 2003 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | 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 |
| spellingShingle | Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees Lavrenyuk, Y.V. Sushchansky, V.I. |
| title | 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_short | Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees |
| title_sort | automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/155723 |
| work_keys_str_mv | AT lavrenyukyv automorphismsofhomogeneoussymmetricgroupsandhierarchomorphismsofrootedtrees AT sushchanskyvi automorphismsofhomogeneoussymmetricgroupsandhierarchomorphismsofrootedtrees |