Math 420/620

Spring 2000

Exam 2

 

  1. Let  be a (the) field of pn elements. Show that is a cyclic group with n elements and is generated by the automorphism  such that

 

  1. Show that there is an irreducible polynomial of any prescribed positive degree over  

 

  1. Show that the multiplicative subgroup of is cyclic.

 

  1. (G) Compute (R,Q).