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# Determining isomorphisms between cyclic groups

Posted on 2011-03-17
Medium Priority
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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.
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Question by:purplesoup
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LVL 37

Expert Comment

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.
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Author Comment

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?
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LVL 37

Accepted Solution

TommySzalapski earned 2000 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.
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