Geodesic
Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees
Algebra and discrete mathematics, no. 4 (2003), pp. 33-49

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{ADM_2003_4_a4,
     author = {Yaroslav V. Lavrenyuk and Vitalii I. Sushchansky},
     title = {Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees},
     journal = {Algebra and discrete mathematics},
     pages = {33--49},
     publisher = {mathdoc},
     number = {4},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2003_4_a4/}
}
TY  - JOUR
AU  - Yaroslav V. Lavrenyuk
AU  - Vitalii I. Sushchansky
TI  - Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees
JO  - Algebra and discrete mathematics
PY  - 2003
SP  - 33
EP  - 49
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/ADM_2003_4_a4/
LA  - en
ID  - ADM_2003_4_a4
ER  - 
%0 Journal Article
%A Yaroslav V. Lavrenyuk
%A Vitalii I. Sushchansky
%T Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees
%J Algebra and discrete mathematics
%D 2003
%P 33-49
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/ADM_2003_4_a4/
%G en
%F ADM_2003_4_a4
Yaroslav V. Lavrenyuk; Vitalii I. Sushchansky. Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees. Algebra and discrete mathematics, no. 4 (2003), pp. 33-49. http://geodesic.mathdoc.fr/item/ADM_2003_4_a4/