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Infinite dimensional linear groups with a large family of G -invariant subspaces

L. A. KurdachenkoA. V. SadovnichenkoI. Ya. Subbotin — 2010

Commentationes Mathematicae Universitatis Carolinae

Let F be a field, A be a vector space over F , GL ( F , A ) be the group of all automorphisms of the vector space A . A subspace B is called almost G -invariant, if dim F ( B / Core G ( B ) ) is finite. In the current article, we begin the study of those subgroups G of GL ( F , A ) for which every subspace of A is almost G -invariant. More precisely, we consider the case when G is a periodic group. We prove that in this case A includes a G -invariant subspace B of finite codimension whose subspaces are G -invariant.

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