Computational group theory and the theory of groups : AMS Special Session on Computational Group Theory, March 3-4, 2007, Davidson College, Davidson, North Carolina
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Bibliographic Information
Computational group theory and the theory of groups : AMS Special Session on Computational Group Theory, March 3-4, 2007, Davidson College, Davidson, North Carolina
（Contemporary mathematics, v. 470）
American Mathematical Society, c2008
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Includes bibliographical references
Description and Table of Contents
Description
The power of general purpose computational algebra systems running on personal computers has increased rapidly in recent years. For mathematicians doing research in group theory, this means a growing set of sophisticated computational tools are now available for their use in developing new theoretical results. This volume consists of contributions by researchers invited to the AMS Special Session on Computational Group Theory held in March 2007. The main focus of the session was on the application of Computational Group Theory (CGT) to a wide range of theoretical aspects of group theory.The articles in this volume provide a variety of examples of how these computer systems helped to solve interesting theoretical problems within the discipline, such as constructions of finite simple groups, classification of $p$-groups via coclass, representation theory and constructions involving free nilpotent groups. The volume also includes an article by R. F. Morse highlighting applications of CGT in group theory and two survey articles. Graduate students and researchers interested in various aspects of group theory will find many examples of Computational Group Theory helping research and will recognize it as yet another tool at their disposal.
Table of Contents
On the application of computational group theory to the theory of groups by R. F. Morse A classification of certain maximal subgroups of alternating groups by B. Benesh On the nonabelian tensor squares of free nilpotent groups of finite rank by R. D. Blyth, P. Moravec, and R. F. Morse Investigating $p$-groups by coclass with GAP by H. Dietrich, B. Eick, and D. Feichtenschlager Homological algebra programming by G. Ellis Groups with a finite covering by siomorphic abelian subgroups by T. S. Foguel and M. F. Ragland On some subnormality conditions in metabelian groups by D. Garrison and L.-C. Kappe Normalizer calculation using automorphisms by A. Hulpke Group theory in SAGE by D. Joyner and D. Kohel Simultaneous constructions of the sporadic groups $\mathsf{Co_2}$ and $\mathsf{Fi_{22}}$ by H. K. Kim and G. O. Michler Constructing simple groups from irreducible subgroups of $GL_n(2)$ by G. O. Michler Dickson polynomials and the norm map between the Hecke algebras of Gelfand-Graev representations by J. G. Rainbolt On orbit equivalent, two-step imprimitive permutation groups by A. Seress and K. Yang.
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