Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 2, pp. 665-676 (2004)

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Indecomposable racks of order $p^2$

Matías Gra\ na

MIT, Mathematics Department, 77 Mass. Ave., 02139 Cambridge, MA - USA, Permanent address: Depto. de Matemática, FCEyN - UBA Pab. I, Ciudad Universitaria, 1428--Buenos Aires, Argentina, e-mail:

Abstract: We classify indecomposable racks of order $p^2$ ($p$ a prime). There are $2p^2-2p-2$ isomorphism classes, among which $2p^2-3p-1$ correspond to quandles. In particular, we prove that an indecomposable quandle of order $p^2$ is affine. As an ingredient of the classification, we prove that the quandle nonabelian second cohomology set of an indecomposable quandle of prime order is trivial.

Classification (MSC2000): 16W30, 57M27

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Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.

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