Cyclic Groups
All cyclic groups of a given order are isomorphic to .
Let G be a cyclic group and n be the order of G. G is then the group generated by . We will show that
Define
- , so that . Clearly, is bijective.
Then
- which proves that .
Read more about this topic: Group Isomorphism
Famous quotes containing the word groups:
“Instead of seeing society as a collection of clearly defined interest groups, society must be reconceptualized as a complex network of groups of interacting individuals whose membership and communication patterns are seldom confined to one such group alone.”
—Diana Crane (b. 1933)
Related Phrases
Related Words