Let F Be A Field Of Characteristic P And Suppose That F L Is Separable And That

Let F be a field of characteristic p and suppose that F ⊂ L is separable and that p divides [L : F].

Suppose furthermore that any q-th root of unity, where q is prime and q ≡ 1 (mod p), that lies in L already lies in F.

Show that F ⊂ L cannot be solvable.

 

"Looking for a Similar Assignment? Get Expert Help at an Amazing Discount!"