摘要
设R是含幺交换环,V是n(n≥2)维自由R-模,W,U是V的非平凡自由R-子模,且V=W U.GL(V/R)是V作为R-模的自同构群,即R上的n级一般线性群.GW,U是GL(V/R)中同时定驻W和U的子群,GW是GL(V/R)中W的定驻子群,显然GW,U是GW的子群.本文定出了在线性群中的全部扩群.
Let R be a commutative ring with unit,V a free R-module of dimension n(n≥2),W,U nontrivial free submodules of V,andV=WU.GL(V/R) denotes the group of automorphisms of V,namely the general linear group of degree n over R,G_(W,U) a subgroup of GL(V/R)which stabilizes both W and U,G_W the stabilizer of W,then obviously G_(W,U) is a subgroup of G_W.In this paper, all the overgroups of G_(W,U) in G_W are determined.
出处
《安徽大学学报（自然科学版）》
CAS
2004年第2期14-18,共5页
Journal of Anhui University(Natural Science Edition)
