  We begin by considering faithful matrix representations of elementary abelian
groups in prime characteristic. The representations considered are seen to be
determined up to change of bases by a single number. Studying this number leads
to a new family of polynomials which exhibit a number of special properties.
These polynomials satisfy a three term recursion and are closely related to
zigzag zero-one sequences. Interpreting the polynomials for the "prime" 1
yields the classical Morgan-Voyce polynomials, which form twoorthogonal
families of polynomials and which have applications in the study of electrical
resistance. Study of the general polynomials reveals deep connections with the
Fibonacci series, the order of appearance of prime numbers in the Fibonacci
sequence, the order of elements in cyclic groups, Artin's conjecture on
primitive roots and the factorization of trinomials over finite fields.
