Finite simple groups : thirty years of the atlas and beyond
著者
書誌事項
Finite simple groups : thirty years of the atlas and beyond
（Contemporary mathematics, 694）
American Mathematical Society, c2017
- タイトル別名
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International conference, finite simple groups : thirty years of the atlas and beyond, celebrating the atlases and honoring John Conway, November 2-5, 2015, Princeton University, Princeton, NJ
Finite simple groups : thirty years of the atlas
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注記
Other editors: Robert Guralnick, Gerhard Hiss, Klaus Lux, Pham Huu Tiep
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
Y.-H. He and J. McKay, Moonshine and the meaning of life
S. P. Norton, The monster is fabulous
A. A. Ivanov, Majorana representation of the monster group
J.-P. Serre, Letter to Donna Testerman
T. Breuer, G. Malle, and E. A. O'Brien, Reliability and reproducibility of Atlas information
F. Lubeck, Characters and Brauer trees of the covering group of $^2E_6(2)$
R. A. Wilson, Maximal subgroups of sporadic groups
R. T. Curtis, Construction of the Thompson chain of subgroups of the Conway group $\cdot$ O and complete graphs on $n$ letters
N. Gill, N. I. Gillespie, C. E. Praeger, and J. Semeraro, Conway's groupoid and its relatives
M. Aschbacher, The subgroup structure of finite groups
K. Magaard, Some remarks on maximal subgroups of finite classical groups
J. F. Carlson, Toward a classification of endotrivial modules
G. Navarro, Some remarks on global/local conjectures
M. Geck, Minuscule weights and Chevalley groups
G. Nebe, R. Parker, and S. E. Rees, A method for building permutation representations of finitely presented groups
M. W. Liebeck, Character ratios for finite groups of Lie type, and applications
A. Shalev, Conjugacy classes, growth and complexity
R. Waldecker, Permutation groups where non-trivial elements have few fixed points.
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