Example 1.3. Non flexible conjugate loop.
1 2 3 4 5 6 7 8
2 1 5 6 7 8 4 3
3 8 6 1 4 2 5 7
4 7 1 5 2 3 8 6
5 3 4 7 8 1 6 2
6 4 8 3 1 7 2 5
7 5 2 8 6 4 3 1
8 6 7 2 3 5 1 4
Many properties that we take for granted in groups do not hold in conjugate
loops. Now we will discuss some properties which conjugate loop fails to satisfy.