 The direct product of two cyclic groups of coprime order is another cyclic group

ID: the-direct-product-of-two-cyclic-groups-of-coprime-order-is-another-cyclic-group

Ciro Santilli 35  Updated 2025-03-28  +Created 1970-01-01

You just map the value (1, 1)

C_{m} \times C_{n}

to the value 1 of

C_{m n}

, and it works out. E.g. for

C_{2} \times C_{3}

, the group generated by of (1, 1) is:

0 = (0, 0)
1 = (1, 1)
2 = (0, 2)
3 = (1, 0)
4 = (0, 1)
5 = (1, 2)
6 = (0, 0) = 0

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