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

Abstract

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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.

How to cite

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Leonid 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 -

References

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