Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Quasinormal Subgroups in Division Rings Radical over Proper Division Subrings

  • Le Qui Danh (Faculty of Mathematics and Computer Science, University of Science, Vietnam National University) ;
  • Trinh Thanh Deo (Faculty of Mathematics and Computer Science, University of Science, Vietnam National University)
  • Received : 2022.08.05
  • Accepted : 2023.05.04
  • Published : 2023.06.30
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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.

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Acknowledgement

The authors would like to thank the referee for his/her useful suggestions. This work was written while the second author was working at the Vietnam Institute for Advanced Study in Mathematics (VIASM). The author would like to thank the institute for providing a fruitful research environment and working condition.

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