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:

    “Only the groups which exclude us have magic.”
    —Mason Cooley (b. 1927)