# S.O.S. Mathematics CyberBoard

Your Resource for mathematics help on the web!
 It is currently Sat, 18 May 2013 08:20:12 UTC

 All times are UTC [ DST ]

 Page 1 of 1 [ 3 posts ]
 Print view Previous topic | Next topic
Author Message
 Post subject: Defition of cyclic groups.Posted: Sun, 8 Apr 2012 01:35:24 UTC
 S.O.S. Oldtimer

Joined: Sat, 21 Jan 2012 03:59:22 UTC
Posts: 182
I'm trying to understand the definition of a cyclic group:
"Cyclic Group: If 'a' is in a group G, and every element of G is a power of 'a' G={a^n : n in Z}, then G is a cyclic group and 'a' is its generator, G=<a>."

What does it mean by "every element of G is a power of 'a' ?" What is a example of this?

Top

 Post subject: Re: Defition of cyclic groups.Posted: Sun, 8 Apr 2012 05:11:27 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 5998
Location: 127.0.0.1, ::1 (avatar courtesy of UDN)
DgrayMan wrote:
I'm trying to understand the definition of a cyclic group:
"Cyclic Group: If 'a' is in a group G, and every element of G is a power of 'a' G={a^n : n in Z}, then G is a cyclic group and 'a' is its generator, G=<a>."

What does it mean by "every element of G is a power of 'a' ?" What is a example of this?

For example, take the group of rotations of a regular n-gon. The rotation about centre by is a generator --- every other rotation is a composite of it or its inverse.

_________________

Top

 Post subject: Re: Defition of cyclic groups.Posted: Sun, 8 Apr 2012 16:02:34 UTC
 S.O.S. Oldtimer

Joined: Sat, 21 Jan 2012 03:59:22 UTC
Posts: 182
I get it. i think typing it, actually helped me sound it out. thanks.

Top

 Display posts from previous: All posts1 day7 days2 weeks1 month3 months6 months1 year Sort by AuthorPost timeSubject AscendingDescending
 Page 1 of 1 [ 3 posts ]

 All times are UTC [ DST ]

#### Who is online

Users browsing this forum: No registered users

 You cannot post new topics in this forumYou cannot reply to topics in this forumYou cannot edit your posts in this forumYou cannot delete your posts in this forum

Search for:
 Jump to:  Select a forum ------------------ High School and College Mathematics    Algebra    Geometry and Trigonometry    Calculus    Matrix Algebra    Differential Equations    Probability and Statistics    Proposed Problems Applications    Physics, Chemistry, Engineering, etc.    Computer Science    Math for Business and Economics Advanced Mathematics    Foundations    Algebra and Number Theory    Analysis and Topology    Applied Mathematics    Other Topics in Advanced Mathematics Other Topics    Administrator Announcements    Comments and Suggestions for S.O.S. Math    Posting Math Formulas with LaTeX    Miscellaneous