Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2015; 52(4): 1353-1363

Printed July 31, 2015

https://doi.org/10.4134/BKMS.2015.52.4.1353

Copyright © The Korean Mathematical Society.

On some subgroups of $D^*$ which satisfy a generalized group identity

Mai Hoang Bien

University of Architecture

Abstract

Let $D$ be a division ring and $w(x_1,x_2,\ldots, x_m)$ be a generalized group monomial over $D^*$. In this paper, we investigate subnormal subgroups and maximal subgroups of $D^*$ which satisfy the identity $w(x_1,x_2,\ldots,x_m)=1$.

Keywords: division ring, subnormal subgroup, maximal subgroup, generalized group identity, group identity

MSC numbers: 16K99, 16R99, 20E28, 20D35

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