Group Isomorphism - Cyclic Groups

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:

    “Women over fifty already form one of the largest groups in the population structure of the western world. As long as they like themselves, they will not be an oppressed minority. In order to like themselves they must reject trivialization by others of who and what they are. A grown woman should not have to masquerade as a girl in order to remain in the land of the living.”
    —Germaine Greer (b. 1939)