主理想整环上线性群中直和因子定驻子群的扩群

Overgroups of the Stabilizer of a Direct Sum Component in the Linear Group Over a Principal Ideal Domain

设R是主理想环 ,V是n维自由R 模 ,W是V的非平凡直和因子 .SL(V/R) ≤G≤GL(V/R) .本文在n≥ 3的情形下定出了W的定驻子群在G中的全部扩群 .

Let R be a principal ideal domain, V a free R -module of dimension n, W a nontrivial direct sum component of V. Let \%SL\%(V/R)≤G≤\%GL\%(V/R). Then all the overgroups of the stabilizer of W in G are determined, for the case n≥3.