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
Datum:2003
Hauptverfasser: Lavrenyuk, Y.V., Sushchansky, V.I.
Format: Artikel
Sprache:English
Veröffentlicht: Інститут прикладної математики і механіки НАН України 2003
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/155723
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
id nasplib_isofts_kiev_ua-123456789-155723
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
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.
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last_indexed 2025-12-07T19:21:01Z
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