219 citations · 799 across the 37 of their papers we have counts for
5 papers · 1 filter
Biquasigroups linear over a group
Wieslaw A. Dudek, Robert A. R. Monzo
We determine the structure of biquasigroups (Q,^,*) satisfying varations of Polonijo's Ward double quasigroup identity (x^z)*(y^z)=x*y, including those that are linear over a group…
Rigid and super rigid quasigroups
Andriy I. Deriyenko, Ivan I. Deriyenko, Wieslaw A. Dudek
The paper deals with quasigroups having a trivial group of automorphisms and a trivial group of autotopisms. Examples of such quasigroups and methods of their verification are give…
On prolongations of quasigroups
Ivan I. Deriyenko, Wieslaw A. Dudek
We prove that any quasigroup admissing complete or quasicomplete mapping has a prolongation to a quasigroup having one element more.
Around the Hosszú-Gluskin theorem for -ary groups
Wieslaw A. Dudek, Kazimierz Glazek
We survey results related to the important Hosszú-Gluskin Theorem on -ary groups adding also several new results and comments. The aim of this paper is to write all such results…
Bi-element representations of ternary groups
Andrzej Borowiec, Wieslaw A. Dudek, Steven Duplij
General properties of ternary semigroups and groups are considered. The bi-element representation theory in which every representation matrix corresponds to a pair of elements is b…