What is the normalizer of the Sylow p-subgroup in the symmetric group Sym(p) generated by the element (1,2,...,p) where p is a prime number?
The Attempt at a Solution
I know that the normalizer has order p(p-1). And I know that it has to include the group generated by (1,2,...,p). I know there must be elements outside <(1,2,...,p)> that conjugates (1,2,...,p) to (1,2,...,p)^n but what are their forms?
Your help will be greatly appreciated.