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Algebra and Discrete Mathematics, 2013, Volume 16, Issue 2, Pages 217–225 (Mi adm448)  
RESEARCH ARTICLE

On some linear groups, having a big family of $G$-invariant subspaces

L. A. Kurdachenko, A. V. Sadovnichenko

Department of Algebra and Geometry, School of Mathematics and Mechanics, National University of Dnepropetrovsk, Gagarin prospect 72, Dnepropetrovsk 10, 49010
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Abstract: 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 $dim_F(BFG/B)$ is finite. In this paper we described the situation when every subspace of $A$ is nearly $G$-invariant.
Keywords: Vector space, linear group, module, $G$-invariant subspace, nearly $G$-invariant subspace.
Received: 13.08.2013
Revised: 13.08.2013
Bibliographic databases:
Document Type: Article
MSC: 15A03, 20F16, 20F29
Language: English
Citation: L. A. Kurdachenko, A. V. Sadovnichenko, “On some linear groups, having a big family of $G$-invariant subspaces”, Algebra Discrete Math., 16:2 (2013), 217–225
Citation in format AMSBIB
\Bibitem{KurSad13}
\by L.~A.~Kurdachenko, A.~V.~Sadovnichenko
\paper On some linear groups, having a big family of $G$-invariant subspaces
\jour Algebra Discrete Math.
\yr 2013
\vol 16
\issue 2
\pages 217--225
\mathnet{http://mi.mathnet.ru/adm448}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=3186085}
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