Texas A&M University, Department of
Mathematics, 216 Milner Hall, 28th of April 2004, 3:00-4:00
Groups and Dynamcs Seminar
On the sum and the
product of two primitive elements of maximal subfields of a finite field
Bogdan Petrenko of University of
Illinois at Urbana-Champaign
If L/K is a field extension, then an element a in L is called its
primitive element if the only subfield of L containing K and a is L.
Let K be a finite field with q elements and L/K an extension of degree p_1p_2p_3,
where p_1, p_2, p_3 are distinct
primes. Let A and B be subfields of L, whose degrees over K are p_1p_2 and
p_1p_3, respectively. Let a and b be primitive elements of the
extensions A/K and B/K, respectively. We investigate two questions:
when K(a+b) = L and when K(a b) = L?