Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 2, pp. 665676 (2004) 

Indecomposable racks of order $p^2$Matías Gra\ naMIT, Mathematics Department, 77 Mass. Ave., 02139 Cambridge, MA  USA, Permanent address: Depto. de Matemática, FCEyN  UBA Pab. I, Ciudad Universitaria, 1428Buenos Aires, Argentina, email: matiasg@math.mit.eduAbstract: We classify indecomposable racks of order $p^2$ ($p$ a prime). There are $2p^22p2$ isomorphism classes, among which $2p^23p1$ 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 Full text of the article:
Electronic version published on: 9 Sep 2004. This page was last modified: 4 May 2006.
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