Examples
- Let R be the group of real numbers under addition. Then the direct product R × R is the group of all two-component vectors (x, y) under the operation of vector addition:
(x1, y1) + (x2, y2) = (x1 + x2, y1 + y2).
- Let G and H be cyclic groups with two elements each:
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- Then the direct product G × H is isomorphic to the Klein four-group:
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G × H * (1, 1) (a, 1) (1, b) (a, b) (1, 1) (1, 1) (a, 1) (1, b) (a, b) (a, 1) (a, 1) (1, 1) (a, b) (1, b) (1, b) (1, b) (a, b) (1, 1) (a, 1) (a, b) (a, b) (1, b) (a, 1) (1, 1)
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Read more about this topic: Direct Product Of Groups
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