%0 Journal Article %1 Grana2002a %A Grana, Matias %D 2004 %J Beiträge Algebra Geom. %K algebra homology quandles %N 2 %P 665--676 %T Indecomposable racks of order p^2 %U http://arxiv.org/abs/math/0203157 %V 45 %X 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 (=Alexander). One of the results yielding this classification is the computation of the quandle nonabelian second cohomology group of an indecomposable quandle of prime order; which turns out to be trivial, as in the abelian case.

@article{Grana2002a, 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 (=Alexander). One of the results yielding this classification is the computation of the quandle nonabelian second cohomology group of an indecomposable quandle of prime order; which turns out to be trivial, as in the abelian case. }, added-at = {2009-05-26T10:50:35.000+0200}, author = {Grana, Matias}, biburl = {https://www.bibsonomy.org/bibtex/2b191855b73743c181efc6efacf261cd5/njj}, description = {Indecomposable racks of order p^2}, interhash = {bcb1b94872c80abbc82668d253a46ee6}, intrahash = {b191855b73743c181efc6efacf261cd5}, journal = {Beitr\"age Algebra Geom.}, keywords = {algebra homology quandles}, number = 2, pages = {665--676}, timestamp = {2009-05-26T10:50:35.000+0200}, title = {Indecomposable racks of order p^2}, url = {http://arxiv.org/abs/math/0203157}, volume = 45, year = 2004 }