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The E-normal structure of odd dimensional unitary groups
K-Theory and Homology · Submitted 29 Jun 2015
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We classify the E-normal subgroups of the groups $U_{2n+1}(R,\Delta)$ (i.e. the subgroups which are normalized by the elementary subgroup $EU_{2n+1}(R,\Delta)$), under the condition that $R$ is either a semilocal or quasifinite ring with involution and $n\geq 3$.
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The abstract, sentence by sentence
In this paper we define odd dimensional unitary groups $U_{2n+1}(R,\Delta)$. 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 $U_{2n}(R,\Lambda)$ where $(R,\Lambda)$ is any form ring. We classify the E-normal subgroups of the groups $U_{2n+1}(R,\Delta)$ (i.e. the subgroups which are normalized by the elementary subgroup $EU_{2n+1}(R,\Delta)$), under the condition that $R$ is either a semilocal or quasifinite ring with involution and $n\geq 3$. Further we investigate the action of $U_{2n+1}(R,\Delta)$ by conjugation on the set of all E-normal subgroups.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In this paper we define odd dimensional unitary groups $U_{2n+1}(R,\Delta)$. | contribution 0.98 | 0.95 | 0.03 | asserted 0.99 |
| s1 | 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 $U_{2n}(R,\Lambda)$ where $(R,\Lambda)$ is any form ring. | background 0.74 | 0.23 | 0.03 | asserted 1.00 |
| s2 | We classify the E-normal subgroups of the groups $U_{2n+1}(R,\Delta)$ (i.e. the subgroups which are normalized by the elementary subgroup $EU_{2n+1}(R,\Delta)$), under the condition that $R$ is either a semilocal or quasifinite ring with involution and $n\geq 3$. | contribution 0.56 | 0.95 | 0.86 | asserted 1.00 |
| s3 | Further we investigate the action of $U_{2n+1}(R,\Delta)$ by conjugation on the set of all E-normal subgroups. | contribution 1.00 | 0.94 | 0.05 | asserted 0.95 |
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Original abstract
In this paper we define odd dimensional unitary groups $U_{2n+1}(R,\Delta)$. 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 $U_{2n}(R,\Lambda)$ where $(R,\Lambda)$ is any form ring. We classify the E-normal subgroups of the groups $U_{2n+1}(R,\Delta)$ (i.e. the subgroups which are normalized by the elementary subgroup $EU_{2n+1}(R,\Delta)$), under the condition that $R$ is either a semilocal or quasifinite ring with involution and $n\geq 3$. Further we investigate the action of $U_{2n+1}(R,\Delta)$ by conjugation on the set of all E-normal subgroups.
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