Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees

• Опубліковано в: : Algebra and Discrete Mathematics
• Дата: 2003
• Автори: Lavrenyuk, Y.V., Sushchansky, V.I.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут прикладної математики і механіки НАН України 2003
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/155723
• Назва журналу: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Цитувати: Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees / Y.V. Lavrenyuk, V.I. Sushchansky // Algebra and Discrete Mathematics. — 2003. — Vol. 2, № 4. — С. 33–49. — Бібліогр.: 13 назв. — англ.

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.