Automorphisms of homogeneous symmetric groups and hierarchomorphisms of rooted trees

• Date: 2018
• Main Authors: Lavrenyuk, Yaroslav V., Sushchansky, Vitalii I.
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: rooted tree; hierarhomorphism; local isometry; diagonal embedding; direct limit; homogeneous symmetric group; group automorphisms; 20B35; 20E08; 20F28; 20F50
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/971
• Journal Title: Algebra and Discrete Mathematics

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 arbitr...