O zovšeobecněních pojmu grupy
Objets simpliciaux
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 .
On (2,2) modular law for ternary GD-groupoids
On -basic quasigroups and their congruences
On 3-semigroups and 3-groups polynomial-derived from integral domains.
On a class of commutative groupoids determined by their associativity triples
Let be a commutative groupoid such that ; ; or . Then is determined uniquely up to isomorphism and if it is finite, then for an integer .
On a class of distributive Steiner quasigroups
On a class of groupoids
On a class of Moufang loops
On a Class of N-ary Quasigroups
On a class of n-ary quasigroups.
On a class of subdirectly irreducible groupoids
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 power of cyclically ordered sets
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.