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:
“As in political revolutions, so in paradigm choicethere is no standard higher than the assent of the relevant community. To discover how scientific revolutions are effected, we shall therefore have to examine not only the impact of nature and of logic, but also the techniques of persuasive argumentation effective within the quite special groups that constitute the community of scientists.”
—Thomas S. Kuhn (b. 1922)
Related Phrases
Related Words