Profinite Group Cogalois Group of a Field Extension Cogalois Theory Continuous 1-Cocycle Kneser Group of Cocycles Cogalois Group of Cocycles Radical Subgroup Hereditarily Radical Subgroup Kneser Subgroup Almost Kneser Subgroup Hereditarily Kneser Subgroup Spectral Space Coherent Map
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 30, No 2-3, (2004), 325p-348p
Given a profinite group Γ acting continuously on a discrete quasi-cyclic group A, certain classes of closed subgroups of Γ (radical, hereditarily radical, Kneser, almost Kneser, and hereditarily Kneser) having natural field theoretic interpretations are defined and investigated. One proves that the hereditarily Kneser subgroups of Γ form a closed subspace of the irreducible spectral space of all closed subgroups of Γ, and a hereditarily Kneser criterion for hereditarily radical subgroups is provided.