Re: [math-fun] Lattice / finite group question
Gene writes: << No. Inversion through the origin is always a lattice isometry, so the isometry group must have even order.
Aha -- good point. Are there further restrictions? --Dan
No. Inversion through the origin is always a lattice isometry, so the isometry group must have even order.
Aha -- good point. Are there further restrictions?
Actually, that inversion is always in the center of the group. So, for example, no (nonabelian) simple group can be the isometry group of a lattice. That seems like enough evidence that the question should be changed to "What groups are isometry groups of lattices?" (instead of phrasing the question in a way that hopes most groups will qualify). --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.
That seems like enough evidence that the question should be changed to "What groups are isometry groups of lattices?" (instead of phrasing the question in a way that hopes most groups will qualify). Me: This question has been studied by many people, of course. See, in particular, the work of Wilhelm Plesken (in MathSciNet, say) NJAS
participants (3)
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dasimov＠earthlink.net -
Michael Kleber -
N. J. A. Sloane