Finite simple exceptional groups of Lie type in which all subgroups of odd index are pronormal-Reference-Cited by-同舟云学术

Finite simple exceptional groups of Lie type in which all subgroups of odd index are pronormal

Published:2020-08-06 Issue:6 Volume:23 Page:999-1016
ISSN:1435-4446
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Kondrat’ev Anatoly S.¹,Maslova Natalia V.²,Revin Danila O.³

Affiliation:

1. Department of Algebra and Topology , Krasovskii Institute of Mathematics and Mechanics UB RAS , Yekaterinburg , Russia

2. Department of Algebra and Topology , Krasovskii Institute of Mathematics and Mechanics UB RAS , Yekaterinburg ; and Ural Federal University, Yekaterinburg , Russia

3. Department of Algebra and Topology , Krasovskii Institute of Mathematics and Mechanics UB RAS , Yekaterinburg ; and Sobolev Institute of Mathematics SB RAS, Novosibirsk; and Novosibirsk State University, Novosibirsk , Russia

Abstract

Abstract A subgroup H of a group G is said to be pronormal in G if H and H g

{H^{g}}

are conjugate in 〈 H , H g 〉

{\langle H,H^{g}\rangle}

for every g ∈ G

{g\in G}

. In this paper, we determine the finite simple groups of type E 6 ⁢ ( q )

{E_{6}(q)}

and E 6 2 ⁢ ( q )

{{}^{2}E_{6}(q)}

in which all the subgroups of odd index are pronormal. Thus, we complete a classification of finite simple exceptional groups of Lie type in which all the subgroups of odd index are pronormal.

Funder

Russian Science Foundation

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Reference21 articles.

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3. D. Gorenstein, Finite Groups, Harper & Row, New York, 1968.

4. D. Gorenstein, R. Lyons and R. Solomon, The Classification of the Finite Simple Groups, Math. Surveys Monogr. 40, American Mathematical Society, Providence, 1994.

5. W. Guo, N. V. Maslova and D. O. Revin, On the pronormality of subgroups of odd index in some extensions of finite groups, Sib. Math. J. 59 (2018), no. 4, 610–622.

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