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A NOTE ON SUBNORMAL SUBGROUPS IN DIVISION RINGS CONTAINING SOLVABLE SUBGROUPS

Part of: Rings and algebras arising under various constructions Structure and classification of infinite or finite groups Division rings and semisimple Artin rings

Published online by Cambridge University Press:  11 January 2023

LE QUI DANH Open the ORCID record for LE QUI DANH [Opens in a new window]  and
TRINH THANH DEO Open the ORCID record for TRINH THANH DEO [Opens in a new window]
LE QUI DANH*
Affiliation:
Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam; Vietnam National University, Ho Chi Minh City, Vietnam and University of Architecture Ho Chi Minh City, 196 Pasteur Street, District 3, Ho Chi Minh City, Vietnam
TRINH THANH DEO
Affiliation:
Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam and Vietnam National University, Ho Chi Minh City, Vietnam e-mail: ttdeo@hcmus.edu.vn
*
e-mail: danh.lequi@uah.edu.vn
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Abstract

Let D be a division ring and N be a subnormal subgroup of the multiplicative group $D^*$. We show that if N contains a nonabelian solvable subgroup, then N contains a nonabelian free subgroup.

Keywords

division ringfree subgroupsolvable subgroupsubnormal subgroup

MSC classification

Primary: 16K20: Finite-dimensional
Secondary: 16S85: Rings of fractions and localizations 16S36: Ordinary and skew polynomial rings and semigroup rings 20E05: Free nonabelian groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 108 , Issue 3 , December 2023 , pp. 422 - 427
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author is funded by Vietnam National University Ho Chi Minh City (VNUHCM) under grant number T2022-18-03.

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