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Abstract

Let D be a division ring with the center F. We say that N is a subgroup of D with understanding that N is in fact a subgroup of the multiplicative group D* of D. In this note we disscus the conjecture which was posed by Herstein in 1978 [2, Conjecture 3]: If N is a subnormal subgroup of D which is radical over F, then N is contained in F. In his paper, Herstein himself showed that the conjecture is true if N is a finite subnormal subgroup of D. However, it is not proven for the general cases. In this note, we establish some properties of subnormal subgroups in division rings which could give some information in the direction of verifying this longstanding conjecture. In particular, it is shown that the conjecture is true for locally centrally finite division rings.



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Issue: Vol 12 No 11 (2009)
Page No.: 5-10
Published: Jun 15, 2009
Section: Article
DOI: https://doi.org/10.32508/stdj.v12i11.2307

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Creative Commons License

Copyright: The Authors. This is an open access article distributed under the terms of the Creative Commons Attribution License CC-BY 4.0., which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

 How to Cite
Nguyen, T., & Bui, H. (2009). ON ONE OF HERSTEIN’S CONJECTURES. Science and Technology Development Journal, 12(11), 5-10. https://doi.org/https://doi.org/10.32508/stdj.v12i11.2307

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