Indecomposable racks of order p^2

Matias Gra\~na

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Indecomposable racks of order p^2

Matias Graña

Quantum Algebra · Submitted 15 Mar 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We classify indecomposable racks of order p^2 (p a prime).

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,608 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.40 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

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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What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We classify indecomposable racks of order p^2 (p a prime).	contribution 0.99	0.96	0.59	asserted 0.99
s1	There are 2p^2 - 2p - 2 isomorphism classes, among which 2p^2 - 3p - 1 correspond to quandles.	result 1.00	0.90	0.38	asserted 1.00
s2	In particular, we prove that an indecomposable quandle of order p^2 is affine (=Alexander).	result 0.99	0.94	0.32	asserted 1.00
s3	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.	result 0.76	0.91	0.05	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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arXiv listing abstract v1

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper

Original 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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