Geodesic
On some linear groups, having a big family of $G$-invariant subspaces
Algebra and discrete mathematics, Tome 16 (2013) no. 2, pp. 217-225.

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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, $G$-invariant subspace, nearly $G$-invariant subspace.
Mots-clés : module 
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L. A. Kurdachenko; A. V. Sadovnichenko. On some linear groups, having a big family of $G$-invariant subspaces. Algebra and discrete mathematics, Tome 16 (2013) no. 2, pp. 217-225. http://geodesic.mathdoc.fr/item/ADM_2013_16_2_a5/

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