$On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup$

On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup

It is proved that if $\pi$-Hall subgroup is a supersolvable group then the derived $\pi$-length of a $\pi$-solvable group $G$ is at most $1+ \max_{r\in \pi}l_r^a(G),$ where $l_r^a(G)$ is the derived $r$-length of a $\pi$-solvable group $G.$

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Datum:	2018
Hauptverfasser:	Monakhov, V. S., Gritsuk, D. V.
Format:	Artikel
Sprache:	English
Veröffentlicht:	Lugansk National Taras Shevchenko University 2018
Schlagworte:	finite group $\pi$-soluble group supersolvable group $\pi$-Hall subgroup derived $\pi$-length 20D10 20D20 20F16
Online Zugang:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1160
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Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	admjournalluguniveduua-article-1160
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spelling	admjournalluguniveduua-article-11602018-05-16T05:04:06Z On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup Monakhov, V. S. Gritsuk, D. V. finite group, $\pi$-soluble group, supersolvable group, $\pi$-Hall subgroup, derived $\pi$-length 20D10, 20D20, 20F16 It is proved that if $\pi$-Hall subgroup is a supersolvable group then the derived $\pi$-length of a $\pi$-solvable group $G$ is at most $1+ \max_{r\in \pi}l_r^a(G),$ where $l_r^a(G)$ is the derived $r$-length of a $\pi$-solvable group $G.$ Lugansk National Taras Shevchenko University 2018-05-16 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1160 Algebra and Discrete Mathematics; Vol 16, No 2 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1160/652 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2018-05-16T05:04:06Z
collection	OJS
language	English
topic	finite group $\pi$-soluble group supersolvable group $\pi$-Hall subgroup derived $\pi$-length 20D10 20D20 20F16
spellingShingle	finite group $\pi$-soluble group supersolvable group $\pi$-Hall subgroup derived $\pi$-length 20D10 20D20 20F16 Monakhov, V. S. Gritsuk, D. V. On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup
topic_facet	finite group $\pi$-soluble group supersolvable group $\pi$-Hall subgroup derived $\pi$-length 20D10 20D20 20F16
format	Article
author	Monakhov, V. S. Gritsuk, D. V.
author_facet	Monakhov, V. S. Gritsuk, D. V.
author_sort	Monakhov, V. S.
title	On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup
title_short	On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup
title_full	On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup
title_fullStr	On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup
title_full_unstemmed	On derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-Hall subgroup
title_sort	on derived $\pi$-length of a finite $\pi$-solvable group with supersolvable $\pi$-hall subgroup
description	It is proved that if $\pi$-Hall subgroup is a supersolvable group then the derived $\pi$-length of a $\pi$-solvable group $G$ is at most $1+ \max_{r\in \pi}l_r^a(G),$ where $l_r^a(G)$ is the derived $r$-length of a $\pi$-solvable group $G.$
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1160
work_keys_str_mv	AT monakhovvs onderivedpilengthofafinitepisolvablegroupwithsupersolvablepihallsubgroup AT gritsukdv onderivedpilengthofafinitepisolvablegroupwithsupersolvablepihallsubgroup
first_indexed	2025-12-02T15:41:58Z
last_indexed	2025-12-02T15:41:58Z
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On derived \(\pi\)-length of a finite \(\pi\)-solvable group with supersolvable \(\pi\)-Hall subgroup

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