The direct product GxH of two

groups G,H is the the group definable on their

Cartesian product by the operation
<g1,h1> . <g2,h2> = <g1.g2 , h1,h2>.

GxH represents the orthogonal combination of G and H:
a group K is isomorphic with GxH iff every member of K
can be written as g.h for some g in G, h in H, and g.h = h.g, then K is isomorphic to GxH.