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A comment on Algebras we love. Parent comment

Re:Algebras we love by rocqua on Monday December 03, 2018 @10:28AM (#18589452)
The additive group of the integers is the set of isomorphisms of a line with evenly spaced points and a direction.

Alternatively, take a directed graph with:

V = The integers

E = {x, y | x - y = 1}

and that graph has the same isomorphism group.

Replace the nodes of that graph with asymmetric graphs, and the resultant undirected graph again has the same isomorphism group.

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Re:Algebras we love by Koshkin on Monday December 03, 2018 @11:31AM (#18590034)
Again, this is only what is called 'a representation.' (The problem with trying to use one as a substitute for the abstract definition is that there usually are many different representations.)
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