Table of Contents
Moufang loops
Abbreviation: MLoop
Definition
A \emph{Moufang loop} is a loops $\mathbf{A}=\langle A,\cdot ,\backslash,/,e\rangle $ such that
$((xy)z)x = x(y(zx))$, $y(x(yz)) = ((yx)y)z$, $(yx)(zy) = (y(xz))y$
Remark:
Morphisms
Let $\mathbf{A}$ and $\mathbf{B}$ be Moufang loops. A morphism from $\mathbf{A}$ to $\mathbf{B}$ is a function $h:A\rightarrow B$ that is a homomorphism:
$h(xy)=h(x)h(y)$, $h(x\backslash y)=h(x)\backslash h(y)$, $h(x/y)=h(x)/h(y)$, $h(e)=e$
Examples
Example 1:
Basic results
Properties
Finite members
$\begin{array}{lr}
f(1)= &1
f(2)= &
f(3)= &
f(4)= &
f(5)= &
f(6)= &
f(7)= &
\end{array}$
