In an informal sense, groups are related to symmetry. I was wondering if there are groups that describe some sort of asymmetry. Does anyone know of such groups or is asymmetry and groups a contradiction in terms?


Thanks a lot 



groups and asymmetry
Maybe it is really a contradiction: once you have a group acting on some set preserving some structure you have a group homomorphism from your group into the automorphism group of that structure. This is really a very general phenomenon.


However, to give you some example which goes perhaps more into your direction: in physical models of solid states you have in crystals a discrete symmetry group of discrete translations by a lattice. Clearly, you would call a crystal "symmetric", historically it is perhaps the origin of all considerations concerning symmetry. But now you perturb the symmetry and spoil your crystal. No lattice acts any more. But if you do that very much you arrive at something similar to a "glas": no obvious symmetry but approximately on a larger scale perhaps, it looks very homogeneous again. In this approximative sense, it might be justifiable to call a glass even translation invariant under all translations.


