Enumeration of nilpotent loops up to isotopy

TL;DR

This paper develops methods to count nilpotent loops of order 2q up to isotopy for odd primes q, extending previous tools to a broader equivalence relation.

Contribution

It adapts existing enumeration tools to count nilpotent loops up to isotopy rather than isomorphism for specific orders.

Findings

Counted nilpotent loops of order 2q up to isotopy for odd primes q

Extended enumeration techniques from isomorphism to isotopy

Provided explicit counts for certain loop orders

Abstract

We modify tools introduced by Daniel Daly and Petr Vojtechovsky in order to count, for any odd prime q, the number of nilpotent loops of order 2q up to isotopy, instead of isomorphy.