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primary groups; coproduct of cyclic groups; almost coproducts; third axiom of countability

References:

[F] Fuchs L.: **Infinite Abelian Groups**. vol. 2, Academic Press, New York, 1973. MR 0349869 | Zbl 0338.20063

[H1] Hill P.: **On the classification of abelian groups**. photocopied manuscript, 1967.

[H2] Hill P.: **Primary groups whose subgroups of smaller cardinality are direct sums of cyclic groups**. Pacific Jour. Math. 42 (1972), 63-67. MR 0315018 | Zbl 0251.20057

[H3] Hill P.: **Units of commutative modular group algebras**. Jour. Pure and Applied Algebra, to appear. MR 1282838 | Zbl 0806.16033

[HM] Hill P., Megibben C.: **On the theory and classification of abelian $p$-groups**. Math. Zeit. 190 (1985), 17-38. MR 0793345 | Zbl 0535.20031

[HU1] Hill P., Ullery W.: **A note on a theorem of May concerning commutative group algebras**. Proc. Amer. Math. Soc. 110 (1990), 59-63. MR 1039530 | Zbl 0704.20007

[K] Kulikov L.: **On the theory of abelian groups of arbitrary power (Russian)**. Mat. Sb. 16 (1945), 129-162. MR 0018180