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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Бібліографічні деталі
Дата:	2003
Автори:	Lavrenyuk, Y.V., Sushchansky, V.I.
Формат:	Стаття
Мова:	English
Опубліковано:	Інститут прикладної математики і механіки НАН України 2003
Назва видання:	Algebra and Discrete Mathematics
Онлайн доступ:	http://dspace.nbuv.gov.ua/handle/123456789/155723
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Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	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

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spelling	irk-123456789-1557232019-06-18T01:25:54Z Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees Lavrenyuk, Y.V. Sushchansky, V.I. 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. 2003 Article 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. http://dspace.nbuv.gov.ua/handle/123456789/155723 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
language	English
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.
format	Article
author	Lavrenyuk, Y.V. Sushchansky, V.I.
spellingShingle	Lavrenyuk, Y.V. Sushchansky, V.I. Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees Algebra and Discrete Mathematics
author_facet	Lavrenyuk, Y.V. Sushchansky, V.I.
author_sort	Lavrenyuk, Y.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
publisher	Інститут прикладної математики і механіки НАН України
publishDate	2003
url	http://dspace.nbuv.gov.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.
series	Algebra and Discrete Mathematics
work_keys_str_mv	AT lavrenyukyv automorphismsofhomogeneoussymmetricgroupsandhierarchomorphismsofrootedtrees AT sushchanskyvi automorphismsofhomogeneoussymmetricgroupsandhierarchomorphismsofrootedtrees
first_indexed	2023-05-20T17:47:05Z
last_indexed	2023-05-20T17:47:05Z
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Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees

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