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Finite group schemes of p-rank ≤ 1

Published online by Cambridge University Press:  27 November 2017

HAO CHANG  and
ROLF FARNSTEINER
HAO CHANG
Affiliation:
Mathematisches Seminar, Christian–Albrechts–Universität zu Kiel, Ludewig–Meyn–Str. 4, 24098 Kiel, Germany. Current address: School of Mathematics and Statistics, Central China Normal University, 430079 Wuhan, People's Republic of China. e-mail: chang@mail.ccnu.edu.cn
ROLF FARNSTEINER
Affiliation:
Mathematisches Seminar, Christian–Albrechts–Universität zu Kiel, Ludewig–Meyn–Str. 4, 24098 Kiel, Germany. e-mail: rolf@math.uni-kiel.de
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Abstract

Let be a finite group scheme over an algebraically closed field k of characteristic char(k) = p ≥ 3. In generalisation of the familiar notion from the modular representation theory of finite groups, we define the p-rank rkp() of and determine the structure of those group schemes of p-rank 1, whose linearly reductive radical is trivial. The most difficult case concerns infinitesimal groups of height 1, which correspond to restricted Lie algebras. Our results show that group schemes of p-rank ≤ 1 are closely related to those being of finite or domestic representation type.

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Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 166 , Issue 2 , March 2019 , pp. 297 - 323
Copyright
Copyright © Cambridge Philosophical Society 2017 

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