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.

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