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:
“Under weak government, in a wide, thinly populated country, in the struggle against the raw natural environment and with the free play of economic forces, unified social groups become the transmitters of culture.”
—Johan Huizinga (18721945)
Related Phrases
Related Words