Atlas of Finite Groups

Atlas of Finite Groups
Title	Atlas of Finite Groups
Editors	John H. Conway; Robert T. Curtis; Simon P. Norton; Richard A. Parker; Robert A. Wilson
Publisher	Oxford University Press
Country	United Kingdom
Language	English
Pub date	1985
Pages	243
Isbn	0-19-853126-6

Atlas of Finite Groups The Atlas of Finite Groups is a reference work that tabulates character tables, subgroup structures, conjugacy classes, and representations for many finite simple groups and related almost simple groups. It serves as a bridge between computational projects in algebra and theoretical work on sporadic groups, linking researchers associated with institutions like the University of Cambridge, University of Oxford, and the University of Birmingham. The volume influenced subsequent work by mathematicians connected to the University of Chicago, Massachusetts Institute of Technology, and Princeton University.

Overview

The Atlas presents systematic information on dozens of finite groups, prominently featuring the twenty-six sporadic groups such as the Monster group, Janko group, Conway group, Fischer group, Baby Monster, and the Mathieu group family. It records character tables, maximal subgroups, and permutation representations for groups studied at research centers including Royal Society, Heriot-Watt University, and Institut des Hautes Études Scientifiques. Mathematicians from projects at institutions like Cambridge University Press and laboratories associated with Harvard University used the Atlas data in investigations that intersected with work by researchers linked to École Normale Supérieure and Moscow State University.

History and development

The project grew from correspondence among group theorists in the 1960s and 1970s, involving figures with ties to University of Oxford, University of Cambridge, University of Manchester, and Imperial College London. Key contributors had collaborations that crossed to researchers at University of California, Berkeley, Princeton University, and University of Illinois Urbana-Champaign. The Atlas compiled data arising from computations using early computer algebra efforts at places like Bell Labs, IBM Research, and facilities connected to Los Alamos National Laboratory. Funding and institutional support involved agencies and societies tied to Royal Society and learned bodies in the United Kingdom and United States.

Contents and structure

The book’s layout organizes entries by group, supplying sections that list generators, orders of conjugacy classes, character tables, and maximal subgroups. For each group the Atlas gives permutation representations and dimensions of irreducible modules relevant to researchers at departments such as Department of Mathematics, University of Oxford and research groups associated with Institute for Advanced Study. Entries also reference construction methods originating from work by mathematicians connected to Cambridge University, Harvard University, and Moscow State University laboratories. The tables support interplay with computational systems developed at institutions like University of Warwick, University of Sydney, and University of Birmingham.

Impact and applications

The Atlas has been foundational for research in algebra, influencing classification projects that involved collaborations across Institute for Advanced Study, Princeton University, and Massachusetts Institute of Technology. It underpins computational systems such as those developed at University of St Andrews and teams linked to University of Leeds and informs proofs and constructions used by researchers at University of Chicago and Rutgers University. Applications extend to work on vertex operator algebras associated with the Monster group that brought together researchers from New York University and University of California, San Diego. The Atlas also catalyzed databases and web projects coordinated by groups at Universität Bonn, ETH Zurich, and Max Planck Institute.

Editions and formats

Originally published in print by Oxford University Press, the Atlas later inspired electronic compilations and CD-ROM projects coordinated by groups at University of Birmingham, University of Sheffield, and teams affiliated with European Mathematical Society. Subsequent formats enabled integration with computational algebra systems developed at Swansea University, Technische Universität Berlin, and University of Sydney. Contributors and editors maintained links to academic publishers and institutions such as Cambridge University Press and research centers at Imperial College London.

Reception and critiques

Scholars at institutions including Princeton University, Harvard University, and University of Cambridge praised the Atlas for rigor and utility, while critiques from some researchers at Moscow State University and groups in continental Europe pointed to gaps in completeness and to errors corrected in later compilations. Debates around data verification prompted follow-up projects at University of Birmingham, University of Leeds, and Queen Mary University of London. The work’s influence is acknowledged in award citations and conference programs organized by entities like the London Mathematical Society and the American Mathematical Society.

Related projects and databases

The Atlas spawned related resources such as online group databases maintained by teams at University of St Andrews, curated lists produced by groups at Mathematical Sciences Research Institute, and computational libraries integrated into systems from GAP developers associated with RWTH Aachen University and contributors at Leibniz University Hannover. Parallel efforts arose at institutions like University of Sydney, University of Warwick, and Universität Stuttgart, and collaborations linked to projects at Max Planck Institute for Mathematics and regional mathematical societies.

Category:Mathematics books