1.2.3 Transitive:
Above loop also shows that transitive property does not hold in conjugate
loops. Here 8 is the conjugate of 6 and 6 is the conjugate of 5 but clearly
8 is not a conjugate of 5. Hence conjugacy is not an equivalence relation in
conjugate loops.
1.3 Conjugate of a subloop
Let L be a conjugate loop, x 2 L and H L: Then the conjugate of H with
respect to x is,
x