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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002186931600017X&_mathId=si1.gif&_user=111111111&_pii=S002186931600017X&_rdoc=1&_issn=00218693&md5=abcfa6d9d5a1dcb1dea04c29a2d82c36" title="Click to view the MathML source">D_kclass="mathContainer hidden">class="mathCode">$D_k$ and investigate the group class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002186931600017X&_mathId=si2.gif&_user=111111111&_pii=S002186931600017X&_rdoc=1&_issn=00218693&md5=c67bda39474d0a6999a2e1cf11e1086e">class="imgLazyJSB inlineImage" height="15" width="51" alt="View the MathML source" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S002186931600017X-si2.gif">class="mathContainer hidden">class="mathCode">$\mathit{Aut}{D}_k$ of automorphisms of this tree. In particular, we characterize the Sylow p  -subgroups in the subgroup class="mathmlsrc">title="View the MathML source" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002186931600017X&_mathId=si3.gif&_user=111111111&_pii=S002186931600017X&_rdoc=1&_issn=00218693&md5=07ec7e88eb2a764a602d3a29a3deabee">class="imgLazyJSB inlineImage" height="18" width="59" alt="View the MathML source" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S002186931600017X-si3.gif">class="mathContainer hidden">class="mathCode">${\mathit{Aut}}_f{D}_p$ 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 class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S002186931600017X&_mathId=si4.gif&_user=111111111&_pii=S002186931600017X&_rdoc=1&_issn=00218693&md5=0ec77f85a585c89baa11ae36a539bab8" title="Click to view the MathML source">FS_Nclass="mathContainer hidden">class="mathCode">$F{S}_{\mathbb{N}}$.