Question

Field theory need help.
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

Answer 1

@FibonacciChick666

Answer 2

oh goodness.

Answer 3

??

Answer 4

ok, so uhm, I don't know if I can help here, I'm gonna have to think on this try @amistre64 or @Hero

Answer 5

@rational may be able to help too

Answer 6

Thanks for the help. ;)

Answer 7

sorry I can't be of more :/

Answer 8

or ganesha ... if memory serves, i wouldnt be able to parse this that well

Answer 9

i judt don't get the whole field of integers modulo p bit.