Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 48, No. 2, pp. 435442 (2007) 

Splitting classes in categories of groupsH. G. Grundman and D. SoltisDepartment of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, USA, email: grundman@brynmawr.edu; Interactive Telecommunications Program, Tisch School of the Arts, New York University, New York, NY 10003, USA, email: ds1935@nyu.eduAbstract: The ideas behind splitting classes were introduced by Freyd and Scedrov in [FS] and expanded by Lippincott in [L]. In the latter work, Lippincott proves that there are exactly six splitting class pairs in the category of sets, but uncountably many in the category of groups. In this paper, we prove much more generally that any category containing the category of finite abelian $p$groups as a full subcategory, for some prime $p$, has uncountably many splitting class pairs. [FS] Freyd, P.; Scedrov, A.: Categories, Allegories. NorthHolland, Amsterdam 1990. [L] Lippincott, L.: Properties preserved by certain classes of morphisms. Preprint. Full text of the article:
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