Finitely presented groups : with applications in post-quantum cryptography and artificial intelligence /

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Bibliographic Details
Edition:	[First edition].
Imprint:	Berlin ; Boston : De Gruyter, [2024] ©2024
Description:	1 online resource (x, 242 pages) : illustrations
Language:	English
Subject:	Group theory. Combinatorial group theory. Logic, Symbolic and mathematical. Cryptography. Artificial intelligence.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/14151763

Hidden Bibliographic Details
Other authors / contributors:	Diekert, Volker, 1955- editor. Kreuzer, Martin, editor.
ISBN:	9783111474274 3111474275 9783111473574 3111473570 9783111473376
Notes:	Includes bibliographical references and index. Online resource; title from PDF title page (ProQuest Ebook Central, viewed January 15, 2025).
Summary:	This book contains surveys and research articles on the state-of-the-art in finitely presented groups for researchers and graduate students. Overviews of current trends in exponential groups and of the classification of finite triangle groups and finite generalized tetrahedron groups are complemented by new results on a conjecture of Rosenberger and an approximation theorem. A special emphasis is on algorithmic techniques and their complexity, both for finitely generated groups and for finite Z-algebras, including explicit computer calculations highlighting important classical methods. A further chapter surveys connections to mathematical logic, in particular to universal theories of various classes of groups, and contains new results on countable elementary free groups. Applications to cryptography include overviews of techniques based on representations of p-groups and of non-commutative group actions. Further applications of finitely generated groups to topology and artificial intelligence complete the volume. All in all, leading experts provide up-to-date overviews and current trends in combinatorial group theory and its connections to cryptography and other areas.

Table of Contents:

Part I: Theory
The universal theories of various classes of groups: a survey
Generalized triangle groups of type (2, 3, 2) with no cyclic essential representations
On countable elementary free groups
Groups elementarily equivalent to the classical matrix groups
An approximation theorem for finitely generated groups
Part II: Algorithms
Some examples of computer calculations with finitely presented groups
An algorithmic survey of finite z-algebras
Complexity of some algorithmic problems in groups: a survey
Part III: Applications
Lifting surface automorphisms in R3 to S3
Secret sharing schemes using representation theory of finite groups
Algebraic messages from the probabilistic entropy principles for knowledge representation in artificial intelligence
Teaching conceptual modeling in the age of generative conversational AI: ideas for a research agenda
Noncommutative group actions for cryptography
Part IV: The life and work of Gerhard Rosenberger
A brief biography
Index.

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