The finite quotients of the multiplicative group of a division algebra of degree 3 are solvable

L. H. Rowen; Y. Segev

doi:10.1007/BF02810692

The finite quotients of the multiplicative group of a division algebra of degree 3 are solvable

L. H. Rowen, Y. Segev

Department of Mathematics

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

5 Scopus citations

Abstract

Let D be a finite dimensional division algebra. It is known that in a variety of cases, questions about the normal subgroup structure of D^x (the multiplicative group of D) can be reduced to questions about finite quotients of D^x. In this paper we prove that when deg(D) = 3, finite quotients of D^x are solvable. The proof uses Wedderburn's Factorization Theorem.

Original language	English
Pages (from-to)	373-380
Number of pages	8
Journal	Israel Journal of Mathematics
Volume	111
DOIs	https://doi.org/10.1007/BF02810692
State	Published - 1 Jan 1999

ASJC Scopus subject areas

General Mathematics

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abstract = "Let D be a finite dimensional division algebra. It is known that in a variety of cases, questions about the normal subgroup structure of Dx (the multiplicative group of D) can be reduced to questions about finite quotients of Dx. In this paper we prove that when deg(D) = 3, finite quotients of Dx are solvable. The proof uses Wedderburn's Factorization Theorem.",

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N2 - Let D be a finite dimensional division algebra. It is known that in a variety of cases, questions about the normal subgroup structure of Dx (the multiplicative group of D) can be reduced to questions about finite quotients of Dx. In this paper we prove that when deg(D) = 3, finite quotients of Dx are solvable. The proof uses Wedderburn's Factorization Theorem.

AB - Let D be a finite dimensional division algebra. It is known that in a variety of cases, questions about the normal subgroup structure of Dx (the multiplicative group of D) can be reduced to questions about finite quotients of Dx. In this paper we prove that when deg(D) = 3, finite quotients of Dx are solvable. The proof uses Wedderburn's Factorization Theorem.

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The finite quotients of the multiplicative group of a division algebra of degree 3 are solvable

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