# Infinite dimensional linear groups with many G - invariant subspaces

Leonid Kurdachenko; Alexey Sadovnichenko; Igor Subbotin

Open Mathematics (2010)

- Volume: 8, Issue: 2, page 261-265
- ISSN: 2391-5455

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topLeonid Kurdachenko, Alexey Sadovnichenko, and Igor Subbotin. "Infinite dimensional linear groups with many G - invariant subspaces." Open Mathematics 8.2 (2010): 261-265. <http://eudml.org/doc/269812>.

@article{LeonidKurdachenko2010,

abstract = {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.},

author = {Leonid Kurdachenko, Alexey Sadovnichenko, Igor Subbotin},

journal = {Open Mathematics},

keywords = {Vector space; Linear groups; Periodic groups; Invariant subspace; infinite-dimensional linear groups; periodic groups; soluble -groups},

language = {eng},

number = {2},

pages = {261-265},

title = {Infinite dimensional linear groups with many G - invariant subspaces},

url = {http://eudml.org/doc/269812},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Leonid Kurdachenko

AU - Alexey Sadovnichenko

AU - Igor Subbotin

TI - Infinite dimensional linear groups with many G - invariant subspaces

JO - Open Mathematics

PY - 2010

VL - 8

IS - 2

SP - 261

EP - 265

AB - 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.

LA - eng

KW - Vector space; Linear groups; Periodic groups; Invariant subspace; infinite-dimensional linear groups; periodic groups; soluble -groups

UR - http://eudml.org/doc/269812

ER -

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