MHB How about this? What is the inverse of a permutation cycle?

[karush]

$\tiny{412.5.9}$
this is under the section on Permutation Groups

What cycle is $(a_1a_2\dots a_n)^{-1}$

ok thot there would be and east theorem on this but can't find

 

[Amer]

How about this? reverse the order

$(a b c d ) (d c b a ) $ a goes to b from the first then the second send b to a.

So

$(a_1 a_2 a_3 a_4 \cdots a_n) (a_n a_{n-1} \cdots a_2 a_1 ) = 1 $