On maximal subgroups of the multiplicative group of a division algebra

R. Hazrat; A. R. Wadsworth

doi:10.1016/j.jalgebra.2009.01.009

On maximal subgroups of the multiplicative group of a division algebra

R. Hazrat, A. R. Wadsworth

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

22 Citations (Scopus)

Abstract

The question of existence of a maximal subgroup in the multiplicative group D* of a division algebra D finite-dimensional over its center F is investigated. We prove that if D* has no maximal subgroup, then deg (D) is not a power of 2, F* 2 is divisible, and for each odd prime p dividing deg (D), 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
DOIs	https://doi.org/10.1016/j.jalgebra.2009.01.009
Publication status	Published - 2009

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10.1016/j.jalgebra.2009.01.009

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title = "On maximal subgroups of the multiplicative group of a division algebra",

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

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

UR - http://handle.uws.edu.au:8081/1959.7/553447

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JO - Journal of Algebra

JF - Journal of Algebra

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ER -

On maximal subgroups of the multiplicative group of a division algebra

Abstract

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