Abstract
M. C. R. Butler, in 1965, proved that if G is a finite rank torsion free abelian group then the following statements are equivalent: (i) G is a pure subgroup of a finite rank completely decomposable group C; (ii) G is a homomorphic image of a finite rank completely decomposable group D; (iii) typeset(G) is finite and for each type τ, G(τ) = Gτ ⨁ < G*(τ) >*, for some τ-homogenous completely decomposable group Gτ, and < G*(τ) >*/G*(τ) is finite.
Research supported, in part, by N.S.F. grant # MCS-8003060.
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List of References
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Arnold, D., Vinsonhaler, C. (1983). Pure Subgroups of Finite Rank Completely Decomposable Groups II. In: Göbel, R., Lady, L., Mader, A. (eds) Abelian Group Theory. Lecture Notes in Mathematics, vol 1006. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21560-9_3
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DOI: https://doi.org/10.1007/978-3-662-21560-9_3
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