# Question: the roots of 1 in characteristic p for p prime...

###### Question details

The roots of 1 in characteristic p for p prime, . To consider .

a) From now on assume . Let K be the spitting field of . Let be the set of roots of 1. is an abelian group, in fact, that and that for . Determine in terms of and .

b) Use your answer to (a) to find when and , and when and .