Solved

Determining isomorphisms between cyclic groups

Posted on 2011-03-17
3
371 Views
Last Modified: 2012-05-11
I have three cyclic groups and need to determine an isomorphism between two of them.

I tried creating Cayley tables for all three groups and coloring in the different numbered squares, but since there are eight elements in each group I'm still finding it difficult to spot which are isomorphic.

Is there a better way to find which are isomorphic?

Note I know this is a pain, but I'd rather not give the actual question as I don't want to just be given the answer, I want to do it for myself, I just need to understand the method to apply.
0
Comment
Question by:purplesoup
  • 2
3 Comments
 
LVL 37

Expert Comment

by:TommySzalapski
ID: 35158576
If you can find a function that maps one group to another, then that's all you need. I would try to find the isomorphic pair by inspection not a Cayley table since you only have three unique pairs to look at.
0
 

Author Comment

by:purplesoup
ID: 35159011
Two of the groups have a modulus multiplier as their operation, the other group has a modulus addition has its operation. What sort of function would map one of these groups to another?
0
 
LVL 37

Accepted Solution

by:
TommySzalapski earned 500 total points
ID: 35159372
Well, all of them should actually be isomorphic assuming they are all the same order (same number of elements). So just pick the two that you can find a mapping for. The two with the modulus multiplier might be the easiest, but without seeing them, it's hard to tell.
0

Featured Post

Is Your Active Directory as Secure as You Think?

More than 75% of all records are compromised because of the loss or theft of a privileged credential. Experts have been exploring Active Directory infrastructure to identify key threats and establish best practices for keeping data safe. Attend this month’s webinar to learn more.

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Suggested Solutions

Complex Numbers are funny things.  Many people have a basic understanding of them, some a more advanced.  The confusion usually arises when that pesky i (or j for Electrical Engineers) appears and understanding the meaning of a square root of a nega…
We are taking giant steps in technological advances in the field of wireless telephony. At just 10 years since the advent of smartphones, it is crucial to examine the benefits and disadvantages that have been report to us.
Along with being a a promotional video for my three-day Annielytics Dashboard Seminor, this Micro Tutorial is an intro to Google Analytics API data.
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.

867 members asked questions and received personalized solutions in the past 7 days.

Join the community of 500,000 technology professionals and ask your questions.

Join & Ask a Question

Need Help in Real-Time?

Connect with top rated Experts

21 Experts available now in Live!

Get 1:1 Help Now