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 SM ISO690:2012ARNAUTOV, Vladimir. About group topologies of the primary Abelian group of finite period which coincide on a subgroup and on the factor group. In: Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2009, nr. 2(60), pp. 19-28. ISSN 1024-7696. |
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| Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica | ||||||
| Numărul 2(60) / 2009 / ISSN 1024-7696 /ISSNe 2587-4322 | ||||||
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| Pag. 19-28 | ||||||
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Let G be any Abelian group of the period pnand 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, τ)/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, τ′) is a topological isomorphism.
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| Cuvinte-cheie Topological group, natural homomorphism, topological isomorphism, subgroup of topological group, factor group of topological group |
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