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.
@article{bwmeta1.element.doi-10_2478_s11533-009-0007-6,
author = {Leonid Kurdachenko and Alexey Sadovnichenko and Igor Subbotin},
title = {On some infinite dimensional linear groups},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {176-185},
zbl = {1193.20062},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0007-6}
}
Leonid Kurdachenko; Alexey Sadovnichenko; Igor Subbotin. On some infinite dimensional linear groups. Open Mathematics, Tome 7 (2009) pp. 176-185. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0007-6/
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