Integral minimalisations improvement for Murphy's polynomial selection algorithm.
On commutative loops of order with metacyclic inner mapping group and trivial center
Using a construction of commutative loops with metacyclic inner mapping group and trivial center described by A. Drápal, we enumerate presumably all such loops of order , for and primes.
On Equational Theory of Left Divisible Left Distributive Groupoids
It is an open question whether the variety generated by the left divisible left distributive groupoids coincides with the variety generated by the left distributive left quasigroups. In this paper we prove that every left divisible left distributive groupoid with the mapping surjective lies in the variety generated by the left distributive left quasigroups.
On left distributive left idempotent groupoids
We study the groupoids satisfying both the left distributivity and the left idempotency laws. We show that they possess a canonical congruence admitting an idempotent groupoid as factor. This congruence gives a construction of left idempotent left distributive groupoids from left distributive idempotent groupoids and right constant groupoids.
Odd order semidirect extensions of commutative automorphic loops
We analyze semidirect extensions of middle nuclei of commutative automorphic loops. We find a less complicated conditions for the semidirect construction when the middle nucleus is an odd order abelian group. We then use the description to study extensions of orders and .
Preface
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