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Article Citation - WoS: 3Lattice-Isomorphic Groups, and Infinite Abelian g-cogalois Field Extensions(World Scientific Publ Co Pte Ltd, 2002) Albu, Toma; Basarab, SerbanThe aim of this paper is to provide a proof of the following result claimed by Albu (Infinite field extensions with Galois-Cogalois correspondence (II), Revue Roumaine Math. Pures Appl. 47 (2002), to appear): The Kneser group Kne(E/F) of an Abelian G-Cogalois extension E/F and the group of continuous characters Ch(Gal(E/F)) of its Galois group Gal(E/F) are isomorphic (in a noncanonical way). The proof we give in this paper explains why such an isomorphism is expected, being based on a classical result of Baer (Amer. J. Math. 61 (1939), 1-44) devoted to the existence of group isomorphisms arising from lattice isomorphisms of their lattices of subgroups.
