Duality of Lines and Planes

Abstract

Consider a finite abelian group A. A mapping

$$ \alpha :A \to A $$

((7.1))

is called a homomorphism of A if it satisfies

$$ \alpha ({\text{a}}{\mkern 1mu} {\text{ + }}{\mkern 1mu} {\text{b}}) = \alpha ({\text{a}}) + \alpha ({\text{b}}),{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\text{a,b}} \in A. $$

((7.2))