Finite groups with 4p2q elements of maximal order

It is an interesting and difficult topic to determine the structure of a finite group by the number of elements of maximal order. This topic is related to Thompson’s conjecture, that is, if two finite groups have the same order type and one of them is solvable, then the other is solvable. In this ar...

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Autores principales:	Tan Sanbiao, Chen Guiyun, Yan Yanxiong
Formato:	article
Lenguaje:	EN
Publicado:	De Gruyter 2021
Materias:	finite groups solvable groups the order of elements 05c25 Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b9d14564e17d438ab8fc3fac7a9ee091
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id	oai:doaj.org-article:b9d14564e17d438ab8fc3fac7a9ee091
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spelling	oai:doaj.org-article:b9d14564e17d438ab8fc3fac7a9ee0912021-12-05T14:10:53ZFinite groups with 4p2q elements of maximal order2391-545510.1515/math-2021-0066https://doaj.org/article/b9d14564e17d438ab8fc3fac7a9ee0912021-08-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0066https://doaj.org/toc/2391-5455It is an interesting and difficult topic to determine the structure of a finite group by the number of elements of maximal order. This topic is related to Thompson’s conjecture, that is, if two finite groups have the same order type and one of them is solvable, then the other is solvable. In this article, we continue this work and prove that if GG is a finite group which has 4p2q4{p}^{2}q elements of maximal order, where pp, qq are primes and 7≤p≤q7\le p\le q, then either GG is solvable or GG has a section who is isomorphic to one of L2(7){L}_{2}\left(7), L2(8){L}_{2}\left(8) or U3(3){U}_{3}\left(3).Tan SanbiaoChen GuiyunYan YanxiongDe Gruyterarticlefinite groupssolvable groupsthe order of elements05c25MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 963-970 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	finite groups solvable groups the order of elements 05c25 Mathematics QA1-939
spellingShingle	finite groups solvable groups the order of elements 05c25 Mathematics QA1-939 Tan Sanbiao Chen Guiyun Yan Yanxiong Finite groups with 4p2q elements of maximal order
description	It is an interesting and difficult topic to determine the structure of a finite group by the number of elements of maximal order. This topic is related to Thompson’s conjecture, that is, if two finite groups have the same order type and one of them is solvable, then the other is solvable. In this article, we continue this work and prove that if GG is a finite group which has 4p2q4{p}^{2}q elements of maximal order, where pp, qq are primes and 7≤p≤q7\le p\le q, then either GG is solvable or GG has a section who is isomorphic to one of L2(7){L}_{2}\left(7), L2(8){L}_{2}\left(8) or U3(3){U}_{3}\left(3).
format	article
author	Tan Sanbiao Chen Guiyun Yan Yanxiong
author_facet	Tan Sanbiao Chen Guiyun Yan Yanxiong
author_sort	Tan Sanbiao
title	Finite groups with 4p2q elements of maximal order
title_short	Finite groups with 4p2q elements of maximal order
title_full	Finite groups with 4p2q elements of maximal order
title_fullStr	Finite groups with 4p2q elements of maximal order
title_full_unstemmed	Finite groups with 4p2q elements of maximal order
title_sort	finite groups with 4p2q elements of maximal order
publisher	De Gruyter
publishDate	2021
url	https://doaj.org/article/b9d14564e17d438ab8fc3fac7a9ee091
work_keys_str_mv	AT tansanbiao finitegroupswith4p2qelementsofmaximalorder AT chenguiyun finitegroupswith4p2qelementsofmaximalorder AT yanyanxiong finitegroupswith4p2qelementsofmaximalorder
_version_	1718371624760115200

Finite groups with 4p2q elements of maximal order

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