On a class of n-ary quasigroups.
On a distance of groups and Latin squares
On a General Associativity Law in Groupoids.
On a generalization of nets
On a planar construction of quasigroups
On a problem of Chern-Akivis-Shelekhov on hexagonal three-webs.
On abelian inner mapping groups of finite loops
In this paper we consider finite loops of specific order and we show that certain abelian groups are not isomorphic to inner mapping groups of these loops. By using our results we are able to construct a finite solvable group of order 120 which is not isomorphic to the multiplication group of a finite loop.
On almost semigroups
On another two cryptographic identities in universal Osborn loops.
On approximation of amenable groups by finite quasigroups.
On -quasigroups.
On binary polynomials in idempotent commutative groupoids
On Bol loops of order
On centerless commutative automorphic loops
In this short paper, we survey the results on commutative automorphic loops and give a new construction method. Using this method, we present new classes of commutative automorphic loops of exponent with trivial center.
On central nilpotency in finite loops with nilpotent inner mapping groups
In this paper we consider finite loops whose inner mapping groups are nilpotent. We first consider the case where the inner mapping group of a loop is the direct product of a dihedral group of order and an abelian group. Our second result deals with the case where is a -loop and is a nilpotent group whose nonabelian Sylow subgroups satisfy a special condition. In both cases it turns out that is centrally nilpotent.
On centrally nilpotent loops
Using a lemma on subnormal subgroups, the problem of nilpotency of multiplication groups and inner permutation groups of centrally nilpotent loops is discussed.
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 congruences and ideals of partially ordered quasigroups
Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.
On dicyclic groups as inner mapping groups of finite loops
Let be a finite group with a dicyclic subgroup . We show that if there exist -connected transversals in , then is a solvable group. We apply this result to loop theory and show that if the inner mapping group of a finite loop is dicyclic, then is a solvable loop. We also discuss a more general solvability criterion in the case where is a certain type of a direct product.
On dihedral 2-groups as inner mapping groups of finite commutative inverse property loops
We show that finite commutative inverse property loops may not have nonabelian dihedral 2-groups as their inner mapping group.