Indecomposable racks of order p²

2002/03/15 by Matias Graña, Graña, Matias · 1 citation
Mathematics · #16W30 #57M27 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Quantum Algebra (math.QA) #math.GT #math.QA #msc:16W30 #msc:57M27

paper · pdf · doi:10.48550/arxiv.math/0203157

8 pages

arxiv created 2002/03/15 · openalex publication_date 2002/03/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We classify indecomposable racks of order p² (p a prime). There are 2p² - 2p - 2 isomorphism classes, among which 2p² - 3p - 1 correspond to quandles. In particular, we prove that an indecomposable quandle of order p² 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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