Configurations of conjugate permutations
We describe some configurations of conjugate permutations which may be used as a mathematical model of some genetical processes and crystal growth.
math.CO↗
arXiv subjects
Ivan I. Deriyenko
Publications and source records attributed to Ivan I. Deriyenko.
D-loops
$D$-loops are loops with the antiautomorphic inverse property. The class of such loops is larger than the class of IP-loops. The smallest $D$-loops which is not an IP-loop has six elements. We prove several basic properties of such loops and present methods of constructions of $D$-loops from IP-loops. Unfortunately, a loop isotopic to a $D$-loop may not be a $D$-loop.
math.GR↗
Rigid and super rigid quasigroups
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 given.
math.GR↗
On prolongations of quasigroups
We prove that any quasigroup admissing complete or quasicomplete mapping has a prolongation to a quasigroup having one element more.
math.GR↗