Subnormal structure of symplectic groups over local rings
type: Item
instance of: scholarly article
title: Subnormal structure of symplectic groups over local rings
zbMATH Open document ID: 0575.20045
DOI: 10.1007/BF01156765
author: S. Tazhetdinov
published in: Mathematical Notes
publication date: 1985-01-01T00:00:00Z
review text: Let R be a local ring, 2 an invertible element of R and Sp(V(R)) the symplectic group of a symplectic finite dimensional space V(R). If I is an ideal of R and \(\lambda_ I: R\to R/I\) is the natural homomorphism, then let \(\pi_ I: Sp(V(R))\to Sp(V(R/I))\) be the natural homomorphism with respect to \(\lambda_ I\). One puts \(GSp(V,I)=(center\) of \(Sp(V(R/I)))\pi_ I^{-1}\), \(SSp(V,I)=(1)\pi_ I^{-1}\). Let \(\rho\in Sp(V(R))\), \(J(R)=(the\) least ideal J such that \(\rho\in GSp(V,J)\). If H is a subgroup of Sp(V(R)) then let \(J(H)=\sum_{\rho \in H}J(\rho).\) In the paper under review the subnormal structure of Sp(V(R)) is studied. The main result of the paper is the following Theorem: If \(H\triangleleft^ dSp(V(R))\) and dim V(R)\(\geq 4\) then \(SSp(V,J^{f(d)})\subseteq H\subseteq GSp(V,J)\), where \(J=J(H)\) and \(f(d)=10^{-1}(11^ d-1)\).
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 3918670
zbMATH Keywords: symplectic group
zbMATH Keywords: symplectic finite dimensional space
MaRDI profile type: Publication
cites work: Symplectic Groups Over Local Rings
cites work: Lineare Gruppen Uber Lokalen Ringen
cites work: Subnormal structure of two-dimensional linear groups over local rings
cites work: Two-Dimensional Linear Groups Over Local Rings
cites work: The subnormal subgroup structure of the infinite symplectic group
cites work: Q4115312
cites work: Q5647103
description: scientific article; zbMATH DE number 3918670