On some infinite dimensional linear groups |
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| Authors: | Leonid A Kurdachenko Alexey V Sadovnichenko Igor Ya Subbotin |
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| Institution: | (1) Department of Algebra, School of Mathematics and Mechanics, National University of Dnepropetrovsk, Dnepropetrovsk, Ukraine;(2) Mathematics Department, National University, Los Angeles, USA |
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| Abstract: | 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 dim
F
(BFG/B) is finite. A subspace B is called almost G-invariant, if dim
F
(B/Core
G
(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.
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| Keywords: | Vector space Linear groups Periodic groups Invariant subspace |
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