This book gives a nice overview of the diversity of current trends in computational and statistical group theory. It presents the latest research and a number of specific topics, such as growth, black box groups, measures on groups, product replacement algorithms, quantum automata, and more. It includes contributions by speakers at AMS Special Sessions at The University of Nevada (Las Vegas) and the Stevens Institute of Technology (Hoboken, NJ).

It is suitable for graduate students and research mathematicians interested in group theory.

Readership

Graduate students and research mathematicians interested in group theory.

Table of Contents

• R. C. Alperin and G. A. Noskov -- Uniform growth, actions on trees and \(GL_2\)
• A. V. Borovik -- Centralisers of involutions in black box groups
• A. V. Borovik, A. G. Myasnikov, and V. Shpilrain -- Measuring sets in infinite groups
• E. M. Freden -- Quantum one-way automata and finitely generated groups
• R. I. Grigorchuk and A. Żuk -- Spectral properties of a torsion-free weakly branch group defined by a three state automaton
• T. Jitsukawa -- Malnormal subgroups of free groups
• C. R. Leedham-Green and S. H. Murray -- Variants of product replacement
• D. V. Osin -- Weakly amenable groups
• C. C. Sims -- The Knuth-Bendix procedure for strings and large rewriting systems