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Normality for elementary subgroup functors

Published online by Cambridge University Press:  24 October 2008

Anthony Bak  and
Nikolai Vavilov
Anthony Bak
Affiliation:
Department of Mathematics, University of Bielefeld, Postfach 10 01 31, 33501 Bielefeld, Germany
Nikolai Vavilov
Affiliation:
Department of Mathematics and Mechanics, University of Sanct-Petersburg, Petrodvorets, 198904, Russia
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Abstract

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 ≥ 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.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 118 , Issue 1 , July 1995 , pp. 35 - 47
Copyright
Copyright © Cambridge Philosophical Society 1995

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