Visual Group Theory, Lecture 4.4: Finitely generated abelian groups

Visual Group Theory, Lecture 4.4: Finitely generated abelian groups We begin this lecture by proving that the cyclic group of order n*m is isomorphic to the direct product of cyclic groups of order n and m if and only if gcd(n,m)=1. Then, we classify all finite abelian groups by decomposing them into a direct product of cyclic groups two different ways (i) the orders of the factors are prime powers, and (ii) by "elementary divisors" -- the order of each factor is a multiple of the order of the next. Finally, we modify this to classify all finitely generated abelian groups. Course webpage (with lecture notes, HW, etc.): http://www.math.clemson.edu/~macaule/math4120-online.html