Enumeration of Nilpotent Loops by Orbit Counting
Abstract
We study central extensions of nilpotent loops by elementary abelian $p$-groups using normalized cocycles. By introducing an affine automorphism group acting on the full cocycle space, we obtain a direct correspondence between affine orbits and isomorphism classes of central extensions. This framework yields an efficient orbit-counting method for enumerating nilpotent loops. We reproduce the known results for orders less than 24, and enumerate the nilpotent loops of order 24 with center of size at least 3.
Fields of Study & Subjects
Finite Group Theory Research
Mathematics and Applications
Advanced Topics in Algebra
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 19 February 2026
- Language
- EN
- Document type
- Preprint