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Quasinormal Subgroups in Division Rings Radical over Proper Division Subrings

Le Qui Danh|Trinh Thanh Deo
경북대학교 자연과학대학 수학과|2023.06|Kyungpook Mathematical Journal|제63권 제2호|pp. 187-198|DOI 10.5666/KMJ.2023.63.2.187

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키워드

radicalnormal subgroupdivision ringquasinormal subgroupMal’cev Neumann
주제분류수학

초록

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

Abstract

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

참고문헌 (22)

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