IMI/Publicaţii/BASM/Ediţii/BASM n.2 (60), 2009/

About group topologies of the primary Abelian group.

Authors: Arnautov Vladimir


Let G be any Abelian group of the period pn and G1 = {g ∈ G|pg = 0}, G2 = {g ∈ G|pn−1g = 0}. If τ and τ′ are a metrizable, linear group topologies such that G2 is a closed subgroup in each of topological groups (G, τ) and (G, τ′), then τ|G2 = τ′|G2 and (G, &tau)/G1 = (G, τ′)/G1 if and only if there exists a group isomorphism φ: G → G such that the following conditions are true:
1. φ'(G2) = G2;
2. g − φ(g) ∈ G1 for any g ∈ G;
3. φ: (G, τ) → (G, &tau′) is a topological isomorphism.



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