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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:
by rocqua 8y ago
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.
- Koshkin 8y agoAgain, 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.)