$Minimal generating sets and Cayley graphs of Sylow $p$-subgroups of finite symmetric groups$

Minimal generating sets and Cayley graphs of Sylow $p$-subgroups of finite symmetric groups

Minimal generating sets of a Sylow $p$-subgroup $P_n$ of the symmetric group $S_{p^n}$ are characterized. The number of ordered minimal generating sets of $P_n$ is calculated. The notion of the type of a generating set of $P_n$ is introduced and it is proved that $P_n$ contains minimal g...

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Datum:	2018
Hauptverfasser:	Slupik, Anna J., Sushchansky, Vitaly I.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Lugansk National Taras Shevchenko University 2018
Schlagworte:	Cayley graph Sylow $p$-subgroup Frattini subgroup 20B35 05C25 05C12 20F65
Online Zugang:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/803
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Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

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spelling	admjournalluguniveduua-article-8032018-04-04T08:49:22Z Minimal generating sets and Cayley graphs of Sylow $p$-subgroups of finite symmetric groups Slupik, Anna J. Sushchansky, Vitaly I. Cayley graph, Sylow $p$-subgroup, Frattini subgroup 20B35, 05C25, 05C12, 20F65 Minimal generating sets of a Sylow $p$-subgroup $P_n$ of the symmetric group $S_{p^n}$ are characterized. The number of ordered minimal generating sets of $P_n$ is calculated. The notion of the type of a generating set of $P_n$ is introduced and it is proved that $P_n$ contains minimal generating sets of all possible type. The isomorphism problem of Cayley graphs of $P_n$ with respect to their minimal generating sets is discussed. Lugansk National Taras Shevchenko University 2018-04-04 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/803 Algebra and Discrete Mathematics; Vol 8, No 4 (2009) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/803/333 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-04-04T08:49:22Z
collection	OJS
language	English
topic	Cayley graph Sylow $p$-subgroup Frattini subgroup 20B35 05C25 05C12 20F65
spellingShingle	Cayley graph Sylow $p$-subgroup Frattini subgroup 20B35 05C25 05C12 20F65 Slupik, Anna J. Sushchansky, Vitaly I. Minimal generating sets and Cayley graphs of Sylow $p$-subgroups of finite symmetric groups
topic_facet	Cayley graph Sylow $p$-subgroup Frattini subgroup 20B35 05C25 05C12 20F65
format	Article
author	Slupik, Anna J. Sushchansky, Vitaly I.
author_facet	Slupik, Anna J. Sushchansky, Vitaly I.
author_sort	Slupik, Anna J.
title	Minimal generating sets and Cayley graphs of Sylow $p$-subgroups of finite symmetric groups
title_short	Minimal generating sets and Cayley graphs of Sylow $p$-subgroups of finite symmetric groups
title_full	Minimal generating sets and Cayley graphs of Sylow $p$-subgroups of finite symmetric groups
title_fullStr	Minimal generating sets and Cayley graphs of Sylow $p$-subgroups of finite symmetric groups
title_full_unstemmed	Minimal generating sets and Cayley graphs of Sylow $p$-subgroups of finite symmetric groups
title_sort	minimal generating sets and cayley graphs of sylow $p$-subgroups of finite symmetric groups
description	Minimal generating sets of a Sylow $p$-subgroup $P_n$ of the symmetric group $S_{p^n}$ are characterized. The number of ordered minimal generating sets of $P_n$ is calculated. The notion of the type of a generating set of $P_n$ is introduced and it is proved that $P_n$ contains minimal generating sets of all possible type. The isomorphism problem of Cayley graphs of $P_n$ with respect to their minimal generating sets is discussed.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/803
work_keys_str_mv	AT slupikannaj minimalgeneratingsetsandcayleygraphsofsylowpsubgroupsoffinitesymmetricgroups AT sushchanskyvitalyi minimalgeneratingsetsandcayleygraphsofsylowpsubgroupsoffinitesymmetricgroups
first_indexed	2025-12-02T15:27:59Z
last_indexed	2025-12-02T15:27:59Z
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Minimal generating sets and Cayley graphs of Sylow \(p\)-subgroups of finite symmetric groups

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