The E-normal structure of odd dimensional unitary groups

2015/06/29 by Anthony Bak, Bak, Anthony, Raimund Preusser +1 · 1 citation
Mathematics · #Finite Group Theory Research #Advanced Topics in Algebra #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1506.08873

Abstract

In this paper we define odd dimensional unitary groups U_2n+1(R,Δ). These groups contain as special cases the odd dimensional general linear groups GL_2n+1(R) where R is any ring, the odd dimensional orthogonal and symplectic groups O_2n+1(R) and Sp_2n+1(R) where R is any commutative ring and further the first author's even dimensional unitary groups U_2n(R,Λ) where (R,Λ) is any form ring. We classify the E-normal subgroups of the groups U_2n+1(R,Δ) (i.e. the subgroups which are normalized by the elementary subgroup EU_2n+1(R,Δ)), under the condition that R is either a semilocal or quasifinite ring with involution and n≥ 3. Further we investigate the action of U_2n+1(R,Δ) by conjugation on the set of all E-normal subgroups.

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