Right quasigroups

Abbreviation: RQgrp

Definition

A right quasigroup is a structure $\mathbf{A}=\langle A,\cdot,/\rangle$ of type $\langle 2,2\rangle $ such that

$(y/x)x = y$

$(xy)/y = x$

Remark:

Morphisms

Let $\mathbf{A}$ and $\mathbf{B}$ be right quasigroups. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:

$h(xy)=h(x)h(y)$, $h(x/y)=h(x)/h(y)$.

Examples

Example 1:

Basic results

Properties

Finite members

$\begin{array}{lr} f(1)= &1\\ f(2)= &3\\ f(3)= &44\\ f(4)= &14022\\ f(5)= &\\ f(6)= &\\ f(7)= &\\ \end{array}$

See http://oeis.org/A193623

Subclasses

Superclasses

References