I'm trouble solving the following question. (note - calculator not allowed)
Prove that this only 1 distinct intermediate subgroup between K = finite field of order 2 adjoined with Theta a root of X^4+X^3+1 & the finite field of order 2.
I attempted to show that the elements fixed by sigma, sigma^2 & sigma^3 are the same (where sigma is the Frobenius map A |---> A^2 ), but I just get lost in calculation! :-s
Is there an easier method?
Many thanks. x