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.
@article{bwmeta1.element.doi-10_2478_s11533-010-0010-y,
author = {Leonid Kurdachenko and Alexey Sadovnichenko and Igor Subbotin},
title = {Infinite dimensional linear groups with many G - invariant subspaces},
journal = {Open Mathematics},
volume = {8},
year = {2010},
pages = {261-265},
zbl = {1207.20048},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0010-y}
}
Leonid Kurdachenko; Alexey Sadovnichenko; Igor Subbotin. Infinite dimensional linear groups with many G - invariant subspaces. Open Mathematics, Tome 8 (2010) pp. 261-265. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-010-0010-y/
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