Talk:Group isomorphism

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Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. References needed. Geometry guy 20:26, 20 May 2007 (UTC)

[edit] Even simpler example

It's not very encyclopedic, I know, but an even simple example is that the group of integers under addition is isomorphic to the group of all even integers under addition. That's an example that a younger person who is unfamiliar with logs can understand: the groups "work the same".

We could also introduce a counterexample - the group generated by flipping a piece of paper horizontally and vertically (the klein 4 group?) is not the same as the group generated by rotating a piece of paper by 90 degrees. The groups "work differently" - in the flipping group, each operation undoes itself if you do it twice, wheras that's not true of the rotation group.

Interestingly - each 4 group has 2 two subgroups that are all isomorphic.

Well - maybe not interesting to you, but possibly interesting to a mathematically inclined 8 or 10 year old.

Paul Murray (talk) 11:59, 26 March 2009 (UTC)