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Algebra and Discrete Mathematics, 2003, Issue 4, Pages 33–49
(Mi adm391)
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This article is cited in 8 scientific papers (total in 8 papers)
RESEARCH ARTICLE
Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees
Yaroslav V. Lavrenyuk, Vitalii I. Sushchansky Kyiv Taras Shevchenko University, Ukraine
Abstract:
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.
Citation:
Yaroslav V. Lavrenyuk, Vitalii I. Sushchansky, “Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees”, Algebra Discrete Math., 2003, no. 4, 33–49
Linking options:
https://www.mathnet.ru/eng/adm391 https://www.mathnet.ru/eng/adm/y2003/i4/p33
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Abstract page: | 165 | Full-text PDF : | 103 | First page: | 1 |
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