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Visual Group Theory A Computer-Oriented Geometric Introduction
This textbook provides an introduction to group theory starting from the basics, relying on geometry to elucidate its various aspects.
Groups...
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Group Theory
This textbook focuses on the basics and complex themes of group theory taught to senior undergraduate mathematics students across universities. The...
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Group Operations
The first section deals with a special class of finite groups which have significance far beyond group theory: groups of permutations. In the two...
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Group Presentations
Groups can be represented by generators and relations, which are products of generators and their inverses that yield the identity element. This...
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Infinite Group Actions on Polyhedra
In the past fifteen years, the theory of right-angled Artin groups and special cube complexes has emerged as a central topic in geometric group...
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The Fundamental Group
Throughout this book, we have established different topological invariants such as connectedness and compactness as tools to classify topological...
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Group Actions
We outline group action and substantiate with various examples. Group action is a potent tool which can be employed to gain insight into the...
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Lie Group
A Lie group is a group (in algebraic sense), which is also a differentiable manifold, with the property that the group operations are compatible with...
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Group Fairness
Assessing whether a model is discriminatory, or not, is a complex problem. As in Chap. 3 , where we...
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Length of the Group Algebra of the Direct Product of a Cyclic Group and a Cyclic P-Group in the Modular Case
In this paper, the length of the group algebra of the direct product of a cyclic group and a cyclic p-group over a field of characteristic p is...
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Differential Calculi in Group Algebras and Group Ends
AbstractGraphs generalizing Cayley graphs and arising from various actions of groups on themselves are studied. A relationship between such graphs...
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Finite Dimensional Group Representations
Algebraic relations among matrices, if any, are encapsulated in their characteristic polynomial. How to decipher this information thus becomes an...
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Galois cohomology and component group of a real reductive group
Let G be a connected reductive group over the field of real numbers ℝ. Using results of our previous joint paper, we compute combinatorially the...
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Hall’s universal group is a subgroup of the abstract commensurator of a free group
P. Hall constructed a universal countable locally finite group U , determined up to isomorphism by two properties: every finite group C is a subgroup...
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An Application of Twisted Group Rings in Secure Group Communications
In this paper we introduce a group key management protocol for secure group communications in a non-commutative setting. To do so, we consider a...
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The Symmetric Group “An Example of Finite Nonabelian Group”
This chapter discusses the group \({\mathfrak{S}}_{n}\) , the symmetric...
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A Gentle Introduction to Group Theory
The book is intended to serve as an introductory course in group theory geared towards second-year university students. It aims to provide them with...
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The de Sitter (dS) Group and Its Representations An Introduction to Elementary Systems and Modeling the Dark Energy Universe
This Second Edition is a comprehensive update, integrating the latest research and theoretical advancements in the field of de Sitter (dS) group...
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Group Homomorphism and Isomorphism
We introduce the notion of homomorphism of groups as a map between two groups which respects the group structure so that we may establish...