Computational Group Theory and the Theory of Groups, Volume II

This volume consists of contributions by researchers who were invited to the Harlaxton Conference on Computational Group Theory and Cohomology, held in August of 2008, and to the AMS Special Session on Computational Group Theory, held in October 2008. This volume showcases examples of how Computational Group Theory can be applied to a wide range of theoretical aspects of group theory. Among the problems studied in this book are classification of $p$-groups, covers of Lie groups, resolutions of Bieberbach groups, and the study of the lower central series of free groups. This volume also includes expository articles on the probabilistic zeta function of a group and on enumerating subgroups of symmetric groups. Researchers and graduate students working in all areas of Group Theory will find many examples of how Computational Group Theory helps at various stages of the research process, from developing conjectures through the verification stage. These examples will suggest to the mathematician ways to incorporate Computational Group Theory into their own research endeavors. Table of Contents: B. Benesh -- The probabilistic Zeta function; B. Eick and T. Rossmann -- Periodicities for graphs of $p$-groups beyond coclass; G. Ellis, H. Mohammadzadeh, and H. Tavallaee -- Computing covers of Lie algebras; D. F. Holt -- Enumerating subgroups of the symmetric group; D. A. Jackson, A. M. Gaglione, and D. Spellman -- Weight five basic commutators as relators; P. Moravec and R. F. Morse -- Basic commutators as relations: a computational perspective; L.-C. Kappe and G. Mendoza -- Groups of minimal order which are not $n$-power closed; L.-C. Kappe and J. L. Redden -- On the covering number of small alternating groups; A. Magidin and R. F. Morse -- Certain homological functors of 2-generator $p$-groups of class 2; M. Roder -- Geometric algorithms for resolutions for Bieberbach groups; F. Russo -- Nonabelian tensor product of soluble minimax groups; J. Schmidt -- Finite groups have short rewriting systems. (CONM/511)