Digital Repository of Luhansk Taras Shevchenko National University
Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees
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| dc.contributor.author | Lavrenyuk, Yaroslav V. | |
| dc.contributor.author | Sushchansky, Vitalii I. | |
| dc.date.accessioned | 2015-10-21T10:32:40Z | |
| dc.date.available | 2015-10-21T10:32:40Z | |
| dc.date.issued | 2003 | |
| dc.identifier.uri | http://hdl.handle.net/123456789/77 | |
| dc.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. | uk_UA |
| dc.language.iso | en | uk_UA |
| dc.publisher | Луганский национальный университет им. Т. Шевченко | uk_UA |
| dc.title | Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees | uk_UA |
| dc.type | Article | uk_UA |
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This is a special issue of the journal devoted to the jubilee of the outstanding Ukrainian and Russian mathematician, one of the founder of our journal Professor Rostislav Grigorchuk, who was 50 years of age on February 23, 2003.