Items related to Groups With Solvable Word Problems (Classic Reprint)
Synopsis
Discover how the word problem in groups links logic, computation, and clear reasoning about algebraic structures.
This book examines how group theory and semigroup theory relate to formal deduction. It offers a method to view group word problems as derivations in equational logic, and it explains how solvable word problems can be built within a rigorous framework. The work combines ideas from logic, algebra, and computation to show how complexity arises in these mathematical systems.
Readers will encounter concepts such as equational systems, decidability, and the Grzegorczyk hierarchy, along with techniques for constructing groups with solvable word problems. The text describes concrete methods for turning semigroups into groups and using functional equations to exhibit decidable structures. It also discusses notable extensions and constructions that help illustrate the boundaries of solvability.
- How equational logic mirrors group and semigroup derivations
- Ways to build groups with a preassigned level of problem-solving difficulty
- Connections between computability, decidability, and algebraic structure
- Examples drawn from HNN extensions and related constructions
Ideal for readers of advanced algebra and theoretical computer science who want a rigorous, accessible path into the interaction between logic and group theory.
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Groups With Solvable Word Problems (Classic Reprint)
Print on DemandSeller: Forgotten Books, London, United Kingdom
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Paperback. Condition: New. Print on Demand. This book explores the fascinating connections between formal systems and the computational complexity of word problems in groups. The author establishes striking analogies between theorems from logic and results about groups, revealing that groups with solvable word problems correspond to decidable systems and simple groups to complete systems. The author investigates the concept of decidability in groups, defining a group as having a word problem in level n of the Grzegorczyk hierarchy if the running time of the algorithm solving the word problem is in 8n. A significant contribution of this book is the construction of finitely presented groups with word problems in 8n (n те 2). This is achieved by utilizing a technique for constructing semigroups following J. Robinson's method of functional equations, which provides a concrete representation of the groups. The author demonstrates that if a semigroup has a word problem in 8n (and not lower), then the resulting group also has a word problem in 8n (and not lower). The insights presented in this book not only contribute to the understanding of word problems in groups but also shed light on the relationship between formal systems and decidability, offering valuable perspectives for further research and applications in computer science and mathematics. This book is a reproduction of an important historical work, digitally reconstructed using state-of-the-art technology to preserve the original format. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in the book. print-on-demand item. Seller Inventory # 9781330197349_0
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Groups With Solvable Word Problems Classic Reprint
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781330197349
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Groups With Solvable Word Problems Classic Reprint
Seller: PBShop.store UK, Fairford, GLOS, United Kingdom
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PAP. Condition: New. New Book. Shipped from UK. Established seller since 2000. Seller Inventory # LW-9781330197349
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