038-2015

MO640 - Multiple-choice question

Let α be a 3-cycle and β be an arbitrary permutation. If two of the elements a, b of α are in the same cycle of β and the third element c is in another cycle of β, we have the following changes from β to the composition αβ :

1. The cycle of β with a and b breaks into two new cycles. The cycle with c remains the same.
2. The cycle with c breaks into two new cycles. The cycle with a and b recombines into a different cycle.
3. These two cycles of β join together into a new cycle.
4. These two cycles of β recombine into two new cycles.
5. None of the above.

Original idea by: Juan Felipe Hernández Albarracín.