On maximal subgroups of the multiplicative group of a division algebra

Roozbeh Hazrat

doi:10.1016/j.jalgebra.2009.01.009

On maximal subgroups of the multiplicative group of a division algebra

Roozbeh Hazrat

School of Mathematics and Physics

Research output: Contribution to journal › Article › peer-review

23 Citations (Scopus)

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Abstract

The question of existence of a maximal subgroup in the multiplicative group of a division algebra D finite-dimensional over its center F is investigated. We prove that if has no maximal subgroup, then is not a power of 2, is divisible, and for each odd prime p dividing , there exist noncyclic division algebras of degree p over F.

Original language	English
Pages (from-to)	2528-2543
Number of pages	16
Journal	Journal of Algebra
Volume	322
Issue number	7
Early online date	12 Feb 2009
DOIs	https://doi.org/10.1016/j.jalgebra.2009.01.009
Publication status	Published - 01 Oct 2009

ASJC Scopus subject areas

Algebra and Number Theory

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On maximal subgroups of the multiplicative group of a division algebra
Copyright 2009 Elsevier. This manuscript is distributed under a Creative Commons Attribution-NonCommercial-NoDerivs License (https://creativecommons.org/licenses/by-nc-nd/4.0/), which permits distribution and reproduction for non-commercial purposes, provided the author and source are cited.
Accepted author manuscript, 257 KBLicence: CC BY-NC-ND

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On maximal subgroups of the multiplicative group of a division algebra

Abstract

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