Infinite abelian groups, whitehead problem and some constructions

  title={Infinite abelian groups, whitehead problem and some constructions},
  author={Saharon Shelah},
  journal={Israel Journal of Mathematics},
  • S. Shelah
  • Published 1974
  • Mathematics
  • Israel Journal of Mathematics
We solve here some problems from Fuchs’ book. We show that the answer to Whitehead’s problem (for groups of power ℵ1) is independent from the usual axioms of set theory. We prove the existence of large rigid systems for groups of power λ, with no restriction on λ. We also prove that there are many non-isomorphic reduced separablep-groups. 
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