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 Algebra Discrete Math.: Year: Volume: Issue: Page: Find

 Algebra Discrete Math., 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

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.

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Bibliographic databases:
MSC: 15A03, 20F16, 20F29
Revised: 13.08.2013
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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{http://www.ams.org/mathscinet-getitem?mr=3186085}