Automorphisms of restricted parabolic trees and Sylow p-subgroups of the finitary symmetric group

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• 作者：Agnieszka Bier^a ; ^{agnieszka.bier@polsl.pl" class="auth_mail" title="E-mail the corresponding author} ; Yuriy Leshchenko^b ; ^{ylesch@ua.fm" class="auth_mail" title="E-mail the corresponding author} ; Vitaliy Sushchanskyy^a ; ^{vitaliy.sushchanskyy@polsl.pl" class="auth_mail" title="E-mail the corresponding author}
• 关键词：20B27 ; 20E08 ; 20B22 ; 20B35 ; 20F65 ; 20B07
• 刊名：Journal of Algebra
• 出版年：2016
• 出版时间：15 April 2016
• 年：2016
• 卷：452
• 期：Complete
• 页码：401-426
• 全文大小：646 K

文摘

In the paper we introduce the notion of a k  -adic restricted parabolic tree D_k$D_k$ and investigate the group $\mathit{Aut}{D}_k$ of automorphisms of this tree. In particular, we characterize the Sylow p  -subgroups in the subgroup ${\mathit{Aut}}_f{D}_p$ of finitary automorphisms of a p-adic restricted parabolic tree. Then we use the characterization for the classification of Sylow p  -subgroups in the finitary symmetric group FS_N$F{S}_{\mathbb{N}}$.