摘要
Let V be a vector space over a field F and G a group of linear transformations in V. It is proved in this note that for any subspace U (V, if dimU/(U∩ g(U))≤ 1, for any g∈G, then there is a g∈ G such that U∩g(U) is a G-invariant subspace, or there is an x∈ V\U such that U + <x> is a G-invariant subspace. So a vector-space analog of Brailovsky's results on quasi-invariant sets is given.
设Ｖ是有限域上Ｆ的向量空间，Ｇ是Ｖ上的线性变换群．本文讨论了Ｖ中拟不变元素的结构·即如果Ｕ是Ｖ中的拟不变元，则存在ｇ∈Ｇ，使得Ｕ∩ｇ（Ｕ）是Ｇ-不变的，或存在ｘ∈ Ｖ＼Ｕ，使得 Ｖ＋＜Ｘ＞是 Ｇ不变的．
基金
Supported by the National Natural Science Foundations of China !(19771014) and Liaoning Province! (972208)
