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http://hdl.handle.net/123456789/77
Title: | Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees |
Authors: | Lavrenyuk, Yaroslav V. Sushchansky, Vitalii I. |
Issue Date: | 2003 |
Publisher: | Луганский национальный университет им. Т. Шевченко |
Description: | A representation of homogeneous symmetric groups by hierarchomorphisms of spherically homogeneous rooted trees are considered. We show that every automorphism of a ho- mogeneous symmetric (alternating) group is locally inner and that the group of all automorphisms contains Cartesian products of ar- bitrary finite symmetric groups. The structure of orbits on the boundary of the tree where inves- tigated for the homogeneous symmetric group and for its automor- phism group. The automorphism group acts highly transitive on the boundary, and the homogeneous symmetric group acts faith- fully on every its orbit. All orbits are dense, the actions of the group on different orbits are isomorphic as permutation groups. |
URI: | http://hdl.handle.net/123456789/77 |
Appears in Collections: | Статті |
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adm-n4-3.pdf | 207.26 kB | Adobe PDF | View/Open |
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