Breaking a cycle into 2 non-disjoint cycles

Question

I have just started reading permutation groups and have gained a basic idea of the topic. I have a cycle of length $5$ given as $(32541)$ and I want to break it into two non-disjoint cycles. I know there can be many such cycles, but is there any way to find non-disjoint cycles of equal length(say $3$)?

Thanks!

Answer 1

Sure:

$$\begin{align} (32541)&=\color{red}{(32)(25)}\color{blue}{(54)(41)}\\ &=\color{red}{(253)}\color{blue}{(154)}. \end{align}$$