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DEMJ
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Homework Statement
List the elements of the cyclic subgroup of [tex]S_6[/tex] generated by
[tex]f = \left(\begin{array}{llllll}
1 & 2 & 3 & 4 & 5 & 6\\
2 & 3 & 4 & 1 & 6 & 5\\
\end{array}\right)[/tex]
Homework Equations
The Attempt at a Solution
I really do not understand what the elements of a permutation really is. I know if I write this as the product of disjoint cycles I get (2341)(65) but other than that I have no idea what the elements could be. The only really element I can say I understand is the identity [tex] \epsilon = \left(\begin{array}{llllll}
1 & 2 & 3 & 4 & 5 & 6\\
1 & 2 & 3 & 4 & 5 & 6\\
\end{array}\right)[/tex] should be an element since it is a subgroup. It also should have an inverse but don't know how to find that.
Please help me get jump started on this problem.