Finite arithmetic subgroups of GLn, II

We continue our investigation on the conjecture of Y. Kitaoka that if a finite subgroup G of GL(n)(O-K) is invariant under the action of Gal(K/Q) then it is contained in GL(n)(K-ab). Here O-K is the ring of integers in a finite Galois extension K of Q and K-ab 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. (C) 2001 Elsevier Science (USA).