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

L. A. Kurdachenko; A. V. Sadovnichenko; I. Ya. Subbotin

Commentationes Mathematicae Universitatis Carolinae (2010)

- Volume: 51, Issue: 4, page 551-558
- ISSN: 0010-2628

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topKurdachenko, L. A., Sadovnichenko, A. V., and Subbotin, I. Ya.. "Infinite dimensional linear groups with a large family of $G$-invariant subspaces." Commentationes Mathematicae Universitatis Carolinae 51.4 (2010): 551-558. <http://eudml.org/doc/246876>.

@article{Kurdachenko2010,

abstract = {Let $F$ be a field, $A$ be a vector space over $F$, $\operatorname\{GL\}(F,A)$ be the group of all automorphisms of the vector space $A$. A subspace $B$ is called almost $G$-invariant, if $\dim _\{F\}(B/\operatorname\{Core\}_\{G\}(B))$ is finite. In the current article, we begin the study of those subgroups $G$ of $\operatorname\{GL\}(F,A)$ 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.},

author = {Kurdachenko, L. A., Sadovnichenko, A. V., Subbotin, I. Ya.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {vector space; linear groups; periodic groups; soluble groups; invariant subspaces; vector space; linear group; periodic group; soluble group; invariant subspace; automorphisms},

language = {eng},

number = {4},

pages = {551-558},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {Infinite dimensional linear groups with a large family of $G$-invariant subspaces},

url = {http://eudml.org/doc/246876},

volume = {51},

year = {2010},

}

TY - JOUR

AU - Kurdachenko, L. A.

AU - Sadovnichenko, A. V.

AU - Subbotin, I. Ya.

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

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2010

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 51

IS - 4

SP - 551

EP - 558

AB - Let $F$ be a field, $A$ be a vector space over $F$, $\operatorname{GL}(F,A)$ be the group of all automorphisms of the vector space $A$. A subspace $B$ is called almost $G$-invariant, if $\dim _{F}(B/\operatorname{Core}_{G}(B))$ is finite. In the current article, we begin the study of those subgroups $G$ of $\operatorname{GL}(F,A)$ 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.

LA - eng

KW - vector space; linear groups; periodic groups; soluble groups; invariant subspaces; vector space; linear group; periodic group; soluble group; invariant subspace; automorphisms

UR - http://eudml.org/doc/246876

ER -

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