Enumeration of nilpotent loops via cohomology |
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Authors: | Daniel Daly,Petr Vojt chovský |
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Affiliation: | aDepartment of Mathematics, University of Denver, 2360 S. Gaylord St., Denver, CO 80208, USA |
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Abstract: | The isomorphism problem for centrally nilpotent loops can be tackled by methods of cohomology. We develop tools based on cohomology and linear algebra that either lend themselves to direct count of the isomorphism classes (notably in the case of nilpotent loops of order 2q, q a prime), or lead to efficient classification computer programs. This allows us to enumerate all nilpotent loops of order less than 24. |
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Keywords: | Nilpotent loop Classification of nilpotent loops Loop cohomology Group cohomology Central extension Latin square |
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