English

Indecomposable racks of order p^2

Quantum Algebra 2007-05-23 v1 Geometric Topology

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.

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Cite

@article{arxiv.math/0203157,
  title  = {Indecomposable racks of order p^2},
  author = {Matias Graña},
  journal= {arXiv preprint arXiv:math/0203157},
  year   = {2007}
}

Comments

8 pages

R2 v1 2026-07-22T16:43:58.937Z