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:

    “If we can learn ... to look at the ways in which various groups appropriate and use the mass-produced art of our culture ... we may well begin to understand that although the ideological power of contemporary cultural forms is enormous, indeed sometimes even frightening, that power is not yet all-pervasive, totally vigilant, or complete.”
    —Janice A. Radway (b. 1949)