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DIGIT PATTERNS AND THE FORMAL ADDITIVE GROUP GREG W. ANDERSON
 

Summary: DIGIT PATTERNS AND THE FORMAL ADDITIVE GROUP
GREG W. ANDERSON
Abstract. We prove an elementary result concerning the relationship be­
tween the multiplicative groups of the coordinate and endomorphism rings of
the formal additive group over a field of characteristic p > 0. Both statement
and proof of the main result involve the combinatorics of base p representations
of positive integers in a striking way.
1. Introduction
Our main result (Theorem 1.2 below) concerns the relationship between the mul­
tiplicative groups of the coordinate and endomorphism rings of the formal additive
group over a field of characteristic p > 0. Our result is elementary and does not
require a great deal of apparatus for its statement. Both statement and proof of the
main result involve the combinatorics of base p representations of positive integers
in a striking way.
1.1. Statement of the main result.
1.1.1. Rings and groups of power series. Fix a prime number p and a field K of
characteristic p. Let q be a power of p. Consider: the (commutative) power series
ring
K[[X ]] = ( #
X i=0

  

Source: Anderson, Greg W. - School of Mathematics, University of Minnesota

 

Collections: Mathematics