abstract algebra permutation

Question

I am dealing with a permutation in the form: $a=\begin{pmatrix}1 &2 &3 &4 &5 &6 \\ 3 &1 &4 &5 &6 &2 \end{pmatrix}$ I am asked to find $|< a >|$ and $a^{100}$. I don't really understand how to do so. Any help would be greatly appreciated! Edit: These questions were on Page 83 of A First Course In Abstract Algebra, by John B. Fraleigh. I don't know what functions the brackets | | or < > are meant to perform.

Answer 1

Decompose $a$ as a product of disjoint cycles: you should find find$$a=(1\,5)(2\,4\,6\,3)$$ Hence the order of $a$ is the l.c.m. of the orders of cycles components, i.e. the l.c.m. of the lengths of the cycles.