ENGLISH

Visual Group Theory: A Computer-Oriented Geometric Introduction

By Stephan Rosebrock

Book information

Publisher
Springer
Year
2024
ISBN
9783662693643, 9783662693650
DOI
10.1007/978-3-662-69365-0
ISSN
2197-4144
Language
english
Format
PDF
Filesize
7 MB (7050048 bytes)
Series
Springer Undergraduate Mathematics Series
Edition
1
Pages
237\244
Topic
Mathematics Algebra
Orientation
yes
Paginated
no
Scanned
portrait
Time added
2024-07-06 10:39:20
Cayley GraphsGAPGroup PresentationsGroup theoryHyperbolic Plane

Description

This textbook provides an introduction to group theory starting from the basics, relying on geometry to elucidate its various aspects. Groups naturally manifest as symmetries of geometric shapes, such as reflections and rotations. The book adopts this perspective to provide a straightforward, descriptive explanation, supported by examples and exercises in GAP, an open-source computer algebra system. It covers all of the key concepts of group theory, including homomorphisms, group operations, presentations, products of groups, and finite, abelian, and solvable groups. The topics include cyclic and symmetric groups, dihedral, orthogonal, and hyperbolic groups, as well as the significant notion of Cayley graphs. Self-contained and requiring little beyond high school mathematics, this book is aimed at undergraduate courses and features numerous exercises. It will also appeal to anyone interested in the geometric approach to group theory.

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