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 Post subject: Re: Separating groups into isomorphism classes.
PostPosted: Sun, 4 Mar 2012 01:53:46 UTC 
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Justin wrote:
Shadow wrote:
Justin wrote:
Ah, right...I guess I'm thinking of something related to the Fundamental Theorem of Abelian Groups(?)
The one where you characterize the (finite) Abelian groups as direct sums up to isomorphism...


Yes you are, and I suspected as much. Don't worry, this is a common mistake when thinking about these things before you really get them all the way down.


LOL...I've been working on getting that for the past six years...some things in math are just harder to digest than others.


If I'm not mistaken you're not in a regular use of group theory though, so it's not as unreasonable for you to not have it quite down yet. :)

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 Post subject: Re: Separating groups into isomorphism classes.
PostPosted: Sun, 4 Mar 2012 01:57:15 UTC 
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Shadow wrote:
If I'm not mistaken you're not in a regular use of group theory though, so it's not as unreasonable for you to not have it quite down yet. :)


True...I always did enjoy analysis more. :wink:

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 Post subject: Re: Separating groups into isomorphism classes.
PostPosted: Sun, 4 Mar 2012 03:01:34 UTC 
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i see some elements match. but on looking at the groups as a whole they don't look like they match.


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 Post subject: Re: Separating groups into isomorphism classes.
PostPosted: Sun, 4 Mar 2012 04:26:45 UTC 
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DgrayMan wrote:
i see some elements match. but on looking at the groups as a whole they don't look like they match.


They do.

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 Post subject: Re: Separating groups into isomorphism classes.
PostPosted: Sun, 4 Mar 2012 07:16:59 UTC 
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which ones are suppose to match. cause i dont see any that do. Also for the group table of Z3xZ2, what is the order that the elements are suppose to go in? For instance i did (0,0), (0,1), (1,0), (1,1), (2,0), and (2,1) in that order for the row side and column side, then filled in the group table. Also what is another way to check if they are isomorphic without making tables?


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 Post subject: Re: Separating groups into isomorphism classes.
PostPosted: Sun, 4 Mar 2012 07:19:32 UTC 
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DgrayMan wrote:
which ones are suppose to match. cause i dont see any that do. Also for the group table of Z3xZ2, what is the order that the elements are suppose to go in? For instance i did (0,0), (0,1), (1,0), (1,1), (2,0), and (2,1) in that order for the row side and column side, then filled in the group table. Also what is another way to check if they are isomorphic without making tables?


The matching ones are Z6 and Z2xZ3.

The order doesn't matter, it's a table, it's just a way to organize data.

From what I understand your best bet is to match up the tables. If you want some more high-tech stuff, it will require more machinery which you don't seem to be comfortable with just yet based on your questions to-date. If you want to try, you can do what I suggested in my last post.

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