I got the following from Wikipedia:
The order of a group is its cardinality, i.e., the number of its elements;
the order, sometimes period, of an element a of a group is the smallest positive integer m such that am = e (where e denotes the identity element of the group, and am denotes the product of m copies of a). If no such m exists, we say that a has infinite order. All elements of finite groups have finite order.
Question: If I have where , is it correct to say that . If so, then contains elements. Must all the elements be distinct? Must an identity be in the group?