On some linear groups, having a big family of \(G\)-invariant subspaces

• Дата: 2018
• Автори: Kurdachenko, L. A., Sadovnichenko, A. V.
• Формат: Стаття
• Мова: English
• Опубліковано: Lugansk National Taras Shevchenko University 2018
• Теми: Vector space; linear group; module; \(G\)-invariant subspace; nearly \(G\)-invariant subspace; 15A03; 20F16; 20F29
• Онлайн доступ: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1158
• Назва журналу: Algebra and Discrete Mathematics

Let \(F\) be a field, \(A\) a vector space over \(F\), \(GL(F, A)\) be the group of all automorphisms of the vector space \(A\). If \(B\) is a subspace of \(A\), then denote by \(BFG\) the \(G\)-invariant subspace, generated by \(B\). A subspace \(B\) is called nearly \(G\)-invariant, if \(dim_F(BFG...