Page "Symmetry group" Paragraph 42

In wider contexts, a symmetry group may be any kind of transformation group, or automorphism group.

Once we know what kind of mathematical structure we are concerned with, we should be able to pinpoint what mappings preserve the structure.

Conversely, specifying the symmetry can define the structure, or at least clarify what we mean by an invariant, geometric language in which to discuss it ; this is one way of looking at the Erlangen programme.