Abstract Algebra: Theory and Applications · Problem 22.4.23

Galois Theory — Thomas Judson

Mathematics — Abstract Algebra · finite-fields-subfields

Problem

Let

E

and

F

be subfields of

\mathrm{GF}(p^n)

. If

|E| = p^r

and

|F| = p^s

, what is the order of

E \cap F