Recent content by postylem

Note that the polynomial factors completely into linears over \mathbb{F}_{16}. Notice that \mathbb{F}_8 is a degree 3 extension of \mathbb{F}_2, and \mathbb{F}_{16} is a degree 4, and \gcd(3,4)=1. That should get you started.

Thinking of this in terms of a http://en.wikipedia.org/wiki/Group_action" is helpful. Showing that the centralizer of cycle a=(1,2,\dots,n) \in S_n, C_{S_n}(a) is equal to the group generated by the cycle of \langle a \rangle, is equivalent to showing that the stabilizer...

oops I just realized that (12345)^2=(13524). I think you are right, Unviaje. I haven't found a proof yet though.

Here is an example in S_5. Take \alpha=(12345), and \beta=(13524). They commute: (12345)(13524)=(14253), (13524)(12345)=(14253). But they are not disjoint (and neither is one a multiple of the other, re Unviaje).