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Displaying similar documents to “On some infinite dimensional linear groups”

Infinite dimensional linear groups with many G - invariant subspaces

Leonid Kurdachenko, Alexey Sadovnichenko, Igor Subbotin (2010)

Open Mathematics

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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 of A is called nearly G-invariant, if dimF(BFG/B) is finite. A subspace B is called almost G-invariant, if dim F(B/Core G(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char F.

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

L. A. Kurdachenko, A. V. Sadovnichenko, I. Ya. Subbotin (2010)

Commentationes Mathematicae Universitatis Carolinae

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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.

RUC systems in rearrangement invariant spaces

P. G. Dodds, E. M. Semenov, F. A. Sukochev (2002)

Studia Mathematica

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We present necessary and sufficient conditions for a rearrangement invariant function space to have a complete orthonormal uniformly bounded RUC system.