Automorphisms of nonsplit extensions of 2-groups by PSL2(𝑞)-Reference-Cited by-同舟云学术

Automorphisms of nonsplit extensions of 2-groups by PSL2(𝑞)

Published:2021-07-08 Issue:6 Volume:24 Page:1245-1261
ISSN:1433-5883
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Revin Danila O.¹,Zavarnitsine Andrei V.²

Affiliation:

1. Sobolev Institute of Mathematics , 4, Koptyug av. , Novosibirsk ; and Novosibirsk State University, 1, Pirogova str., 630090, Novosibirsk; and Krasovskii Institute of Mathematics and Mechanics, 16, Kovalevskaya str., 620990, Ekaterinburg , Russia

2. Sobolev Institute of Mathematics , 4, Koptyug av. 630090 , Novosibirsk , Russia

Abstract

Abstract We complete the description of automorphism groups of all nonsplit extensions of elementary abelian 2-groups by PSL 2 ⁢ ( q )

\mathrm{PSL}_{2}(q)

, with 𝑞 odd, for an irreducible induced action. An application of this result to the theory of 𝜋-submaximal subgroups is given.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2021-0067/pdf

Reference17 articles.

1. V. P. Burichenko, Extensions of abelian 2-groups by means of L 2 ⁢ ( q ) L_{2}(q) with irreducible action, Algebra Logic 39 (2000), no. 3, 160–183.

2. R. Burkhardt, Die Zerlegungsmatrizen der Gruppen PSL ⁢ ( 2 , p f ) \mathrm{PSL}(2,p^{f}) , J. Algebra 40 (1976), no. 1, 75–96.

3. W. Guo and D. O. Revin, Classification and properties of the 𝜋-submaximal subgroups in minimal nonsolvable groups, Bull. Math. Sci. 13 (2018), no. 2, 325–351.

4. W. Guo and D. O. Revin, On maximal and submaximal 𝔛-subgroups, Algebra Logic 57 (2018), no. 1, 9–28.

5. W. Guo and D. O. Revin, Pronormality and submaximal 𝔛-subgroups on finite groups, Commun. Math. Stat. 6 (2018), no. 3, 289–317.

Cited by 2 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. On $ \pi $-Submaximal Subgroups of Minimal Nonsolvable Groups;Siberian Mathematical Journal;2022-09

2. AUTOMORPHISMS OF NONSPLIT COVERINGS OF PSL₂ (q) IN ODD CHARACTERISTIC DIVIDING q - 1;SIB ELECTRON MATH RE;2022