For each prime number p, let $F_p$ denote the field of integers modulo p. Now let K be any finite field. a) Prove that K contains a subfield isomorphic to $F_p$ for some prime number p b) Prove that the intersection of all of the subfields of K will be isomorphic to $F_p$ for some prime number p c) Prove that the cardinality of K is equal to a power of p for some prime number p
I do not understand the question. Can someone explain me, please? To me, $F_p = Z_p $ and $char Z_p= p$ and the finite field K has characteristic = another prime, namely $p_1$. I do not see the link between them.