Please use this identifier to cite or link to this item: 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
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