Talk:Group isomorphism

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)

Circle-dot symbol

What does the odot mean e.g. in f(u * v) = f(u) \odot f(v)? Len loker (talk) 01:07, 1 January 2014 (UTC)

I don't think the syntax, (G, ∗) and (H, $\odot$), is very clear. In most standard textbooks, the multiplication convention is used and the group operator isn't spelled out explicitly. ImTheIP (talk) 16:18, 30 October 2018 (UTC)