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Order (group theory)
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Order (group theory)
In group theory, a branch of mathematics, the term order is used in two unrelated senses:
- The order of a group is its cardinality, i.e., the number of elements in its set. Also, the order, sometimes period, of an element a of a group is the smallest positive integer m such that (where e denotes the identity element of the group, and am denotes the product of m copies of a). If no such m exists, a is said to have infinite order.
- The ordering relation of a partially or totally ordered group.
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