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 arbitr...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/971 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua:article-9712018-05-14T07:18:11Z Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees Lavrenyuk, Yaroslav V. Sushchansky, Vitalii I. rooted tree, hierarhomorphism, local isometry, diagonal embedding, direct limit, homogeneous symmetric group, group automorphisms 20B35, 20E08, 20F28, 20F50 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 inves-tigated 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. Lugansk National Taras Shevchenko University 2018-05-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/971 Algebra and Discrete Mathematics; Vol 2, No 4 (2003) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/971/500 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-05-14T07:18:11Z |
| collection |
OJS |
| language |
English |
| topic |
rooted tree hierarhomorphism local isometry diagonal embedding direct limit homogeneous symmetric group group automorphisms 20B35 20E08 20F28 20F50 |
| spellingShingle |
rooted tree hierarhomorphism local isometry diagonal embedding direct limit homogeneous symmetric group group automorphisms 20B35 20E08 20F28 20F50 Lavrenyuk, Yaroslav V. Sushchansky, Vitalii I. Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees |
| topic_facet |
rooted tree hierarhomorphism local isometry diagonal embedding direct limit homogeneous symmetric group group automorphisms 20B35 20E08 20F28 20F50 |
| format |
Article |
| author |
Lavrenyuk, Yaroslav V. Sushchansky, Vitalii I. |
| author_facet |
Lavrenyuk, Yaroslav V. Sushchansky, Vitalii I. |
| author_sort |
Lavrenyuk, Yaroslav V. |
| title |
Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees |
| 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 |
| 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 inves-tigated 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/971 |
| work_keys_str_mv |
AT lavrenyukyaroslavv automorphismsofhomogeneoussymmetricgroupsandhierarchomorphismsofrootedtrees AT sushchanskyvitaliii automorphismsofhomogeneoussymmetricgroupsandhierarchomorphismsofrootedtrees |
| first_indexed |
2025-07-17T10:34:53Z |
| last_indexed |
2025-07-17T10:34:53Z |
| _version_ |
1837890070224306176 |