Abbreviation: RQgrp

A \emph{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:

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:

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

Example 1:

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

See http://oeis.org/A193623

Right loops

Quasigroups