Quasinormal Subgroups in Division Rings Radical over Proper Division Subrings

The motivation for this study comes from a question posed by I.N. Herstein in the Israel Journal of Mathematics in 1978. Specifically, let D be a division ring with center F. The aim of this paper is to demonstrate that every quasinormal subgroup of the multiplicative group of D, which is radical ov...

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Bibliographic Details
Published inKyungpook mathematical journal Vol. 63; no. 2; pp. 187 - 198
Main Authors Le Qui Danh, Trinh Thanh Deo
Format Journal Article
LanguageKorean
Published 2023
Subjects
normal subgroup
radical
quasinormal subgroup
Mal'cev-Neumann
division ring
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Summary:The motivation for this study comes from a question posed by I.N. Herstein in the Israel Journal of Mathematics in 1978. Specifically, let D be a division ring with center F. The aim of this paper is to demonstrate that every quasinormal subgroup of the multiplicative group of D, which is radical over some proper division subring, is central if one of the following conditions holds: (i) D is weakly locally finite; (ii) F is uncountable; or (iii) D is the Mal'cev-Neumann division ring.
Bibliography:KISTI1.1003/JNL.JAKO202322252268767
ISSN:1225-6951
0454-8124