# Abstract Algebra-Isomorphism

by TheForumLord
Tags: abstract, algebraisomorphism
 P: 352 Use the internal characterization of direct products of groups: if $$G$$ has two normal subgroups $$H, K$$ such that $$HK = G$$ and $$H \cap K = 1$$, then $$G \cong H \times K$$. Also, the third isomorphism theorem may help you (if $$K \subset H$$ are both normal subgroups of $$G$$, then $$G/H \cong (G/K)/(H/K)$$).