On some infinite dimensional linear groups

• Autorzy: Leonid Kurdachenko , Alexey Sadovnichenko , Igor Subbotin
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Vector space; Linear groups; Periodic groups; Invariant subspace

Kategorie tematyczne

• 20F16: Solvable groups, supersolvable groups
• 15A03: Vector spaces, linear dependence, rank
• 20F29: Representations of groups as automorphism groups of algebraic systems

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2009
• Tom: 7
• Numer: 2
• Strony: 176-185

Daty

wydano

2009-06-01

online

2009-05-24

Twórcy

autor

Leonid Kurdachenko

• Department of Algebra, School of Mathematics and Mechanics, National University of Dnepropetrovsk, Dnepropetrovsk, Ukraine

autor

Alexey Sadovnichenko

• Department of Algebra, School of Mathematics and Mechanics, National University of Dnepropetrovsk, Dnepropetrovsk, Ukraine

autor

Igor Subbotin

• Mathematics Department, National University, Los Angeles, USA

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-009-0007-6