Titlebook: Exercises in Abelian Group Theory; Grigore Călugăreanu,Simion Breaz,Dumitru Vălcan Book 2003 Springer Science+Business Media Dordrecht 200

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Torsion-free groupsIn this Chapter we shall use several results.

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Mixed groupsA mixed group . (. is a . ) if there exists a direct decomposition . with . a torsion-free group. . is called a . if it has a bounded index subgroup which splits. We mention the following results:

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Subgroup lattices of groupsTwo elements . in a poset (., ≤) axe called . if . or .. A . of a poset . is called . or a . if any two elements in . are comparable.

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Book 2003ematics and Computer Science,‘Babes-Bolyai‘ University in Cluj-Napoca, Romania. From 1992,these lectures were extended to a twosemester electivecourse on abelian groups for undergraduate stu­ dents, followed by a twosemester course on the same topic for graduate students in Algebra. All the other au

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Topological groupsre called open .. A subset . of . is said to be a ciosed set if the set . is open. If . ⊆ . the set B̄ = n{F | F is closed, . ⊆ . called .. Clearly . ⊆ . is closed if and only if . = .. If . ⊆ . the set .. = {. n . | . ∈ .} is a topology on ., called the relative . induced by . on ..