Finite Arithmetic Subgroups of GLn, II Original Research Article

We continue our investigation on the conjecture of Y. Kitaoka that if a finite subgroup G of GLn(OK) is invariant under the action ofGal(K/image) then it is contained in GLn(Kab). Here OK is the ring of integers in a finite Galois extension K of image and Kab is the maximal abelian subextension of K. We give a very precise description of a hypothetical counterexample of minimal order for minimal possible n. Using it we prove the conjecture for n=3 and give a new, simplified proof for n=2.