In group theory, a branch of mathematics, the term order is used in two unrelated senses:
<span><span>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 <span>am = e</span> (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.</span><span>The ordering relation of a partially or totally ordered group.</span></span>
This article is about the first sense of order.
The order of a group G is denoted by ord(G) or | G | and the order of an element a is denoted by ord(a) or | a |.
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