Abstract Algebra: Theory and Applications · Problem 13.13

Group Actions — Thomas Judson

Mathematics — Abstract Algebra · finite-abelian-groups

Problem

Let

G

H

, and

K

be finitely generated abelian groups. Show that if

G \times H \cong G \times K

, then

H \cong K

. Give a counterexample to show that this cannot be true in general.