Thread: Composite permutation multiplication

In the following composite permutation multiplication I got the value 1 repeatedly. Is it true? If false, plz explain me....

....| 2 1 4 6 | | 6 5 1 9 | | 2 1 3 4 | | 6 9 |
g=| 1 4 6 2 | | 5 1 9 6 | | 1 3 9 6 | | 9 6 | means g=( 2 1 4 6 ) ( 6 5 1 9 ) ( 2 1 3 4 ) ( 6 9 )

...| 2 6 5 1 7 | | 6 1 2 5 4 3 | |2 4 6 7 |
f=| 6 5 1 7 2 | | 1 2 5 4 3 6 | |4 6 7 2 | means f= ( 2 6 5 1 7 ) ( 6 1 2 5 4 3 ) (2 4 6 7 )


g o f= | 1 2 3 4 5 .......|
.........| 2 6 4 1 1 .......|

Plz reply me as soon as possible

Thanks,
Sophia

Permutations are bijections, in particular, injections. So two different numbers cannot be mapped to 1.