Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 48, No. 2, pp. 435-442 (2007)
Splitting classes in categories of groups
H. G. Grundman and D. SoltisDepartment of Mathematics, Bryn Mawr College, Bryn Mawr, PA 19010, USA, e-mail: firstname.lastname@example.org; Interactive Telecommunications Program, Tisch School of the Arts, New York University, New York, NY 10003, USA, e-mail: email@example.com
Abstract: 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. North-Holland, Amsterdam 1990. [L] Lippincott, L.: Properties preserved by certain classes of morphisms. Preprint.
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Electronic version published on: 7 Sep 2007. This page was last modified: 28 Jun 2010.