Finite rational matrix groups / G. Nebe, W. Plesken.

Format:

Book

Author/Creator:

Nebe, G. (Gabriele), 1967- author.

Plesken, Wilhelm, 1950- author.

Series:

Memoirs of the American Mathematical Society ; Volume 116, Number 556.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 116, Number 556

Language:

English

Subjects (All):

Finite groups.

Integral representations.

Forms, Quadratic.

Physical Description:

1 online resource (158 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1995.

Language Note:

English

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.

Contents:

""Table of Contents""; ""Finite rational matrix groups""; ""I. Introduction""; ""II. Notation, basic definitions, and constructions""; ""III. Methods""; ""IV. Odd dimensions""; ""V. Groups of type L[sub(2)](p) of degree p±l""; ""VI. Dimensions 2[sub(p)]""; ""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""; ""List of notations""; ""References""; ""Finite rational matrix groups of degree 16""; ""I. Introduction""

""II. Methods: Invariant quadratic forms and subgroups""""III. The simplicial complexes M[sup(irr)][sub(8)](Q) and M[sup(irr,F)][sub(8)](Q)""; ""IV. Results in dimension 16""; ""V. Determination of the primitive r.i.m.f. groups of degree 16""; ""VI. The simplicial complexes M[sup(irr}][sub(16)](Q) and M[sup(irr,F)][sub(16)](Q)""; ""Appendix: The Gram matrices fixed by the primitive r.i.m.f groups of degree 16""; ""References""

Notes:

Description based upon print version of record.

Includes bibliographical references at the end of each chapters and index.

Description based on print version record.

ISBN:

1-4704-0135-5