# Difficult Question on Permutations

1. Jan 31, 2009

### PhysicsHelp12

If you have a permutation writtein disjoint cycle notation ( I attatched it )

what's the minimum positive integer k such that t^k =Identity

t is tau

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2. Feb 1, 2009

### CompuChip

Can you reason what will happen when $\tau$ is multiplied by itself? And if you calculate $\tau^3$?
What will happen in general when we keep multiplying tau by itself?

3. Feb 1, 2009

Remember that disjoint cycles commute. Thus, if $\tau = \tau_1 \tau_2 \dotsc \tau_m$ is a product of disjoint cycles, then $\tau^n = \tau_1^n \tau_2^n \dotsc \tau_m^n$.