Finite Arithmetic Subgroups ofGLn Original Research Article

We discuss the following conjecture of Kitaoka:If a finite subgroup G of GLn(OK)is invariant under the action ofGal(K/image) then it is contained inGLn(Kab). HereOKis the ring of integers in a finite Galois extensionKof image andKabis the maximal abelian subextension ofK. Our main result reduces this conjecture to a special case of elementary abelianp-groupsG. Also, we construct some new examples which negatively answer a question of Y. Kitaoka.