Definition of cyclic group Algebraic structures
(Monday, May 3, 2010)
The group A generated by the single element a e G a described in the lemma (multiplicatively) is called a cyclic group of G or simply a cyclic group and a is called a generator of a.
The order of an element a e G is the order of the cyclic subgroup A Ì G and is the smallest positive integer n for which an = e, and if an ¹ e, for n e Z, then the order of a (or A itself) is said to be infinite, the group composition being multiplication. Similarly, a cyclic group can be generated by a single element additively, were each element of the cyclic group is some multiple of the generator.
Posted in Posted by waytofeed at 7:36 AM
0 comments:
Post a Comment