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Finite rational matrix groups

About this Title

G. Nebe and W. Plesken

Publication: Memoirs of the American Mathematical Society
Publication Year: 1995; Volume 116, Number 556
ISBNs: 978-0-8218-0343-1 (print); 978-1-4704-0135-1 (online)
DOI: https://doi.org/10.1090/memo/0556
MathSciNet review: 1265024
MSC: Primary 20H20; Secondary 11E57

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Table of Contents

Chapters

  • Finite rational matrix groups
  • I. Introduction
  • II. Notation, basic definitions, and constructions
  • III. Methods
  • IV. Odd dimensions
  • V. Groups of type $L_2(p)$ of degree $p \pm 1$
  • VI. Dimensions $2p$
  • VII. Dimension 12
  • VIII. Dimension 18
  • IX. Dimension 20
  • Appendix. The Gram matrices fixed by the primitive r.i.m.f. groups of degree $n=12,14,15,18,20,21$ and $22$
  • Finite rational matrix groups of degree $16$
  • I. Introduction
  • II. Methods: Invariant quadratic forms and subgroups
  • III. The simplicial complexes $M^{irr}_8(\mathbb {Q})$ and $M^{irr,F}_8(\mathbb {Q})$
  • IV. Results in dimension 16
  • V. Determination of the primitive r.i.m.f. groups of degree 16
  • VI. The simplicial complexes $M^{irr}_{16}(\mathbb {Q})$ and $M^{irr,F}_{16}(\mathbb {Q})$
  • Appendix. The Gram matrices fixed by the primitive r.i.m.f. groups of degree $16$