Reduced fusion systems over 2-groups of sectional rank at most 4 / Bob Oliver.

Format:

Book

Author/Creator:

Oliver, Robert, 1949- author.

Series:

Memoirs of the American Mathematical Society ; v. 239, no. 1131.

Memoirs of the American Mathematical Society, 0065-9266 ; volume 239, number 1131

Language:

English

Subjects (All):

Finite groups.

Finite simple groups.

Algebraic topology.

Physical Description:

1 online resource (112 pages).

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, [2015]

Language Note:

Text in English.

Summary:

The author classifies all reduced, indecomposable fusion systems over finite 2-groups of sectional rank at most 4. The resulting list is very similar to that by Gorenstein and Harada of all simple groups of sectional 2-rank at most 4. But this method of proof is very different from theirs, and is based on an analysis of the essential subgroups which can occur in the fusion systems.

Contents:

Cover

Title page

Introduction

Chapter 1. Background on fusion systems

1.1. Essential subgroups in fusion systems

1.2. Reduced fusion systems

1.3. The focal subgroup

Chapter 2. Normal dihedral and quaternion subgroups

Chapter 3. Essential subgroups in 2-groups of sectional rank at most 4

3.1. Essential subgroups of index 4 in their normalizer

3.2. Essential pairs of type \II

3.3. Essential subgroups of index 2 in

Chapter 4. Fusion systems over 2-groups of type ₂( )

Chapter 5. Dihedral and semidihedral wreath products

Chapter 6. Fusion systems over extensions of \UT₃(4)

Appendix A. Background results about groups

Appendix B. Subgroups of 2-groups of sectional rank 4

Appendix C. Some explicit 2-groups of sectional rank 4

Appendix D. Actions on 2-groups of sectional rank at most 4

Bibliography

Back Cover.

Notes:

"Volume 239, number 1131 (third of 6 numbers), January 2016."

Includes bibliographical references and index.

Description based on print version record.

ISBN:

1-4704-2745-1