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2022 Locally solvable and solvable-by-finite maximal subgroups of GLn(D)
Huynh Viet Khanh, Bui Xuan Hai
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Publ. Mat. 66(1): 77-97 (2022). DOI: 10.5565/PUBLMAT6612203

Abstract

This paper aims to study solvable-by-finite and locally solvable maximal subgroups of an almost subnormal subgroup of the general skew linear group GLn(D) over a division ring D. It turns out that in the case where D is non-commutative, if such maximal subgroups exist, then either it is abelian or [D : F]<. Also, if F is an infinite field and n5, then every locally solvable maximal subgroup of a normal subgroup of GLn(F) is abelian.

Funding Statement

This work is funded by Vietnam National University HoChiMinh City (VNUHCM) under grant number B2020-18-02

Funding Statement

This work is funded by Vietnam National University HoChiMinh City (VNUHCM) under grant number B2020-18-02

Funding Statement

This work is funded by Vietnam National University HoChiMinh City (VNUHCM) under grant number B2020-18-02

Citation

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Huynh Viet Khanh. Bui Xuan Hai. "Locally solvable and solvable-by-finite maximal subgroups of GLn(D)." Publ. Mat. 66 (1) 77 - 97, 2022. https://doi.org/10.5565/PUBLMAT6612203

Information

Received: 18 February 2020; Accepted: 20 July 2020; Published: 2022
First available in Project Euclid: 4 January 2022

Digital Object Identifier: 10.5565/PUBLMAT6612203

Subjects:
Primary: 12E15 , 16K20 , 16K40 , 20E25

Keywords: division ring , locally solvable group , maximal subgroup , polycyclic-by-finite group

Rights: Copyright © 2022 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.66 • No. 1 • 2022
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