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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De Gruyter
2021-08-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2021-0066 |
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doaj-b9d14564e17d438ab8fc3fac7a9ee0912021-10-03T07:42:36ZengDe GruyterOpen Mathematics2391-54552021-08-0119196397010.1515/math-2021-0066Finite groups with 4p2q elements of maximal orderTan Sanbiao0Chen Guiyun1Yan Yanxiong2School of Mathematics and Statistics, Southwest University, Chongqing, 400715, P. R. ChinaSchool of Mathematics and Statistics, Southwest University, Chongqing, 400715, P. R. ChinaSchool of Mathematics and Statistics, Southwest University, Beibei, Chongqing, 400715, P. R. ChinaIt 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).https://doi.org/10.1515/math-2021-0066finite groupssolvable groupsthe order of elements05c25 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Tan Sanbiao Chen Guiyun Yan Yanxiong |
| spellingShingle |
Tan Sanbiao Chen Guiyun Yan Yanxiong Finite groups with 4p2q elements of maximal order Open Mathematics finite groups solvable groups the order of elements 05c25 |
| 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 |
| series |
Open Mathematics |
| issn |
2391-5455 |
| publishDate |
2021-08-01 |
| 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). |
| topic |
finite groups solvable groups the order of elements 05c25 |
| url |
https://doi.org/10.1515/math-2021-0066 |
| work_keys_str_mv |
AT tansanbiao finitegroupswith4p2qelementsofmaximalorder AT chenguiyun finitegroupswith4p2qelementsofmaximalorder AT yanyanxiong finitegroupswith4p2qelementsofmaximalorder |
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