Displaying similar documents to “Infinite dimensional linear groups with many G - invariant subspaces”

On some infinite dimensional linear groups

Leonid Kurdachenko, Alexey Sadovnichenko, Igor Subbotin (2009)

Open Mathematics

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Let F be a field, A be a vector space over F, and GL(F,A) 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 dimF(B/CoreG(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF. ...

Groups with Restricted Conjugacy Classes

de Giovanni, F., Russo, A., Vincenzi, G. (2002)

Serdica Mathematical Journal

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Let F C 0 be the class of all finite groups, and for each nonnegative integer n define by induction the group class FC^(n+1) consisting of all groups G such that for every element x the factor group G/CG ( <x>^G ) has the property FC^n . Thus FC^1 -groups are precisely groups with finite conjugacy classes, and the class FC^n obviously contains all finite groups and all nilpotent groups with class at most n. In this paper the known theory of FC-groups is taken as a model, and it...

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.