Cyclic group:Z12

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VIEW FACTS ABOUT THIS GROUP: All factsGroup property satisfactionsSubgroup property satisfactionsGroup property dissatisfactionsSubgroup property satisfactions
VIEW DEFINITIONS USING THIS AS EXAMPLE: All terms |Group properties |Subgroup properties|
VIEW FACTS USING THIS AS EXAMPLE: All facts |Group property non-implications |Subgroup property non-implications |Group metaproperty dissatisfactionsSubgroup metaproperty dissatisfactions

Definition

This group, denoted $C_{12},{\mathbb{Z}}_{12}$ or $\mathbb{Z}/12\mathbb{Z}$, is defined in the following equivalent ways:

1. It is a cyclic group of order $12$.
2. It is the direct product of the cyclic group of order three and the cyclic group of order four.