PUB - Publikationen an der Universität Bielefeld

We define a notion of group functor G on categories of graded modules, which unifies previous concepts of a group functor G possessing a notion of elementary subfunctor E. We show under a general condition which is easily checked in practice that the elementary subgroup E(M) of G(M) is normal for all quasi-weak Noetherian objects M in the source category of G. This result includes all previous ones on Chevalley and classical groups G of rank greater than or equal to 2 over a commutative or module finite ring M (since such rings are quasi-weak Noetherian) and settles positively unanswered cases of normality for these group functors.