Topology of Numbers · Problem 7.3.1

The Class Group for Quadratic Forms — Allen Hatcher

Mathematics — Number Theory · converse-cyclic-product-groups

Problem

Show the converse of Proposition 7.8: If a product

G_1 \times G_2

of finite abelian groups is cyclic then

G_1

and

G_2

are cyclic of coprime orders.