When there is only a single element in , is usually written as . In this case, is the cyclic subgroup of the powers of , a cyclic group, and we say this group is generated by . Equivalent to saying an element generates a group is saying that equals the entire group . For finite groups, it is also equivalent to saying that has order .
When there is only a single element in , is usually written as . In this case, is the cyclic subgrou!p of the powers of , a cyclic group, and we say this grou?p is generated by . Equivalent to saying an element generates a group is saying that equals the entire group . For finite groups, it is also equivalent to saying that has order .