Finite rational matrix groups

The study of finite rational matrix groups reduces to the investigation of the maximal finite irreducible matrix groups and their natural lattices, which often turn out to have rather beautiful geometric and arithmetic properties. This book presents a full classification in dimensions up to 23 and w...

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Bibliographic Details
Main Authors Nebe, G, Plesken, Wilhelm
Format eBook
LanguageEnglish
Published Providence, R.I American Mathematical Society 1995
Edition1
SeriesMemoirs of the American Mathematical Society
Subjects
Finite groups
Forms, Quadratic
Integral representations
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Summary:The study of finite rational matrix groups reduces to the investigation of the maximal finite irreducible matrix groups and their natural lattices, which often turn out to have rather beautiful geometric and arithmetic properties. This book presents a full classification in dimensions up to 23 and with restrictions in dimensions and p +1 and p-1 for all prime numbers p. Nonmaximal finite groups might act on several types of lattices and therefore embed into more than one maximal finite group. This gives rise to a simplicial complex interrelating the maximal finite groups and measuring the complexity of the dimension. Group theory, integral representation theory, arithmetic theory of quadratic forms and algorithmic methods are used.
Bibliography:Access is restricted to licensed institutions
July 1995, Volume 116, number 556 (third of 4 numbers).
Electronic reproduction.
Providence, Rhode Island
Description based on print version record.
American Mathematical Society.
2012
Includes bibliographical references (p. 144).
Mode of access : World Wide Web
ISBN:0821803433
9780821803431