Indecomposable racks of order p2
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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.