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Book DetailsContemporary MathematicsVolume: 694; 2017; 229 ppMSC: Primary 01; 05; 17; 20
This volume contains the proceedings of the international conference Finite Simple Groups: Thirty Years of the Atlas and Beyond Celebrating the Atlases and Honoring John Conway, which was held from November 2–5, 2015, at Princeton University, Princeton, New Jersey.
Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics.
The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.
ReadershipGraduate students and research mathematicians interested in algebra, group theory, representation theory, combinatorics, coding theory, number theory, and algebraic geometry.

Table of Contents

Articles

YangHui He and John McKay — Moonshine and the meaning of life

Simon P. Norton — The Monster is fabulous

A. A. Ivanov — Majorana representation of the Monster group

JeanPierre Serre — Letter to Donna Testerman

Thomas Breuer, Gunter Malle and E. A. O’Brien — Reliability and reproducibility of Atlas information

Frank Lübeck — Characters and Brauer trees of the covering group of ${{}^2\!E_6(2)}$

Robert A. Wilson — Maximal subgroups of sporadic groups

R. T. Curtis — Construction of the Thompson Chain of subgroups of the Conway group $\cdot {\mathrm O}$ and complete graphs on $n$ letters

Nick Gill, Neil I. Gillespie, Cheryl E. Praeger and Jason Semeraro — Conway’s groupoid and its relatives

Michael Aschbacher — The subgroup structure of finite groups

Kay Magaard — Some remarks on maximal subgroups of finite classical groups

Jon F. Carlson — Toward a classification of endotrivial modules

Gabriel Navarro — Some remarks on global/local conjectures

Meinolf Geck — Minuscule weights and Chevalley groups

Gabriele Nebe, Richard Parker and Sarah Rees — A method for building permutation representations of finitely presented groups

Martin W. Liebeck — Character ratios for finite groups of Lie type, and applications

Aner Shalev — Conjugacy classes, growth and complexity

Rebecca Waldecker — Permutation groups where nontrivial elements have few fixed points


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This volume contains the proceedings of the international conference Finite Simple Groups: Thirty Years of the Atlas and Beyond Celebrating the Atlases and Honoring John Conway, which was held from November 2–5, 2015, at Princeton University, Princeton, New Jersey.
Classification of Finite Simple Groups, one of the most monumental accomplishments of modern mathematics, was announced in 1983 with the proof completed in 2004. Since then, it has opened up a new and powerful strategy to approach and resolve many previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the Atlas of Finite Groups (John H. Conway et al.), and in An Atlas of Brauer Characters (Christoph Jansen et al.). It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in the everyday life of researchers in many areas of contemporary mathematics.
The main objective of the conference was to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. The papers in this volume are based on talks given at the conference. They present a comprehensive survey on current research in all of these fields.
Graduate students and research mathematicians interested in algebra, group theory, representation theory, combinatorics, coding theory, number theory, and algebraic geometry.

Articles

YangHui He and John McKay — Moonshine and the meaning of life

Simon P. Norton — The Monster is fabulous

A. A. Ivanov — Majorana representation of the Monster group

JeanPierre Serre — Letter to Donna Testerman

Thomas Breuer, Gunter Malle and E. A. O’Brien — Reliability and reproducibility of Atlas information

Frank Lübeck — Characters and Brauer trees of the covering group of ${{}^2\!E_6(2)}$

Robert A. Wilson — Maximal subgroups of sporadic groups

R. T. Curtis — Construction of the Thompson Chain of subgroups of the Conway group $\cdot {\mathrm O}$ and complete graphs on $n$ letters

Nick Gill, Neil I. Gillespie, Cheryl E. Praeger and Jason Semeraro — Conway’s groupoid and its relatives

Michael Aschbacher — The subgroup structure of finite groups

Kay Magaard — Some remarks on maximal subgroups of finite classical groups

Jon F. Carlson — Toward a classification of endotrivial modules

Gabriel Navarro — Some remarks on global/local conjectures

Meinolf Geck — Minuscule weights and Chevalley groups

Gabriele Nebe, Richard Parker and Sarah Rees — A method for building permutation representations of finitely presented groups

Martin W. Liebeck — Character ratios for finite groups of Lie type, and applications

Aner Shalev — Conjugacy classes, growth and complexity

Rebecca Waldecker — Permutation groups where nontrivial elements have few fixed points