Automorphisms Of Product Of Finite P Groups With Applications To Algebraic Topology
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Automorphisms of Product of Finite P-groups with Applications to Algebraic Topology
In addition to several examples and applications which apply the major results of the thesis to a collection of familiar finite groups, this work includes three appendices which relate the group-theoretic properties previously invoked to all finite 2-groups through order 32, and summarizes the occurrences of these properties in all finite 2-groups through order 64.
Groups St Andrews 2013
Author: C. M. Campbell
language: en
Publisher: Cambridge University Press
Release Date: 2015-10-22
Leading researchers survey the latest developments in group theory and many related areas.
The Compressed Word Problem for Groups
Author: Markus Lohrey
language: en
Publisher: Springer Science & Business Media
Release Date: 2014-04-04
The Compressed Word Problem for Groups provides a detailed exposition of known results on the compressed word problem, emphasizing efficient algorithms for the compressed word problem in various groups. The author presents the necessary background along with the most recent results on the compressed word problem to create a cohesive self-contained book accessible to computer scientists as well as mathematicians. Readers will quickly reach the frontier of current research which makes the book especially appealing for students looking for a currently active research topic at the intersection of group theory and computer science. The word problem introduced in 1910 by Max Dehn is one of the most important decision problems in group theory. For many groups, highly efficient algorithms for the word problem exist. In recent years, a new technique based on data compression for providing more efficient algorithms for word problems, has been developed, by representing long words over group generators in a compressed form using a straight-line program. Algorithmic techniques used for manipulating compressed words has shown that the compressed word problem can be solved in polynomial time for a large class of groups such as free groups, graph groups and nilpotent groups. These results have important implications for algorithmic questions related to automorphism groups.