Solved

Determining isomorphisms between cyclic groups

Posted on 2011-03-17
3
378 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
[X]
Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

  • Help others & share knowledge
  • Earn cash & points
  • Learn & ask questions
  • 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

Free Tool: ZipGrep

ZipGrep is a utility that can list and search zip (.war, .ear, .jar, etc) archives for text patterns, without the need to extract the archive's contents.

One of a set of tools we're offering as a way to say thank you for being a part of the community.

Question has a verified solution.

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

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…
This article provides a brief introduction to tissue engineering, the process by which organs can be grown artificially. It covers the problems with organ transplants, the tissue engineering process, and the current successes and problems of the tec…
Although Jacob Bernoulli (1654-1705) has been credited as the creator of "Binomial Distribution Table", Gottfried Leibniz (1646-1716) did his dissertation on the subject in 1666; Leibniz you may recall is the co-inventor of "Calculus" and beat Isaac…
I've attached the XLSM Excel spreadsheet I used in the video and also text files containing the macros used below. https://filedb.experts-exchange.com/incoming/2017/03_w12/1151775/Permutations.txt https://filedb.experts-exchange.com/incoming/201…

728 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