On commutative A-loops of order PQ
Abstract
We study a construction introduced by Drápal, giving rise to commutative A-loops of order kn where k and n are odd numbers. We show which combinations of k and n are possible if the construction is based on a field or on a cyclic group. We conclude that if p and q are odd primes, there exists a non-associative commutative A-loop of order pq if and only if p divides q2 - 1 and such a loop is most probably unique.
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