Abstract
In the past six years two excellent articles have appeared that survey developments in the theory of mixed abelian groups. I refer to the papers of Warfield that appear in the proceedings of the 1976 Las Cruces conference on abelian groups [WRF2], and in the proceedings of the 1981 Oberwolfach conference on abelian groups [WRF3]. Because of this it is not necessary to dwell at length here on the theory of mixed groups as it developed until 1981. That leaves 1981 and 1982. As it usually takes me at least a couple of years to catch up on the literature, let alone the preprints and the gossip, I will not attempt a serious survey of the field. Instead I will take a quick look at the history of the subject, knowing that Warfield’s papers can be used to correct any serious misrepresentations that I make. Then I will give an overview of the general theory, illustrating it by a generalization of the notion a (global) Warfield group based on a class of pure subgroups of finite rank completely decomposable torsion-free groups that admit a complete set of invariants.
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Richman, F. (1983). Mixed Groups. 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_28
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