Finitely Presented Groups: With Applications in Post-Quantum Cryptography and Artificial Intelligence

Finitely Presented Groups: With Applications in Post-Quantum Cryptography and Artificial Intelligence
Author: Volker Diekert (Editor), Martin Kreuzer (Editor)
Publisher finelybook 出版社:‏ De Gruyter
Edition 版本:‏ 1st
Publication Date 出版日期:‏ 2024-10-07
Language 语言: English
Print Length 页数: 252 pages
ISBN-10: 3111473376
ISBN-13: 9783111473376

Book Description

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.