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) ...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.展开更多
基金Supported by the National Natural Science Foundations of China !(19771014) and Liaoning Province! (972208)
文摘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.