Abstract Algebra: Group Theory
N.B. Singh
This audiobook is narrated by a digital voice.
"Abstract Algebra: Group Theory" is an introductory textbook designed for absolute beginners seeking a foundational understanding of abstract algebra through the lens of group theory. This comprehensive guide navigates through the fundamental concepts, including group definitions, subgroup classifications, normal subgroups, quotient groups, and explores advanced topics such as group actions, Sylow theorems, solvable groups, nilpotent groups, free groups, group presentations, commutator subgroups, and their applications. Written with clarity and accessibility in mind, it equips readers with essential theoretical knowledge and practical problem-solving skills, making it an indispensable resource for students and enthusiasts alike delving into the elegant and abstract world of group theory.
Duration - 3h 54m.
Author - N.B. Singh.
Narrator - Digital Voice Mary G.
Published Date - Monday, 20 January 2025.
Copyright - © 2024 N.B. Singh ©.
Location:
United States
Description:
This audiobook is narrated by a digital voice. "Abstract Algebra: Group Theory" is an introductory textbook designed for absolute beginners seeking a foundational understanding of abstract algebra through the lens of group theory. This comprehensive guide navigates through the fundamental concepts, including group definitions, subgroup classifications, normal subgroups, quotient groups, and explores advanced topics such as group actions, Sylow theorems, solvable groups, nilpotent groups, free groups, group presentations, commutator subgroups, and their applications. Written with clarity and accessibility in mind, it equips readers with essential theoretical knowledge and practical problem-solving skills, making it an indispensable resource for students and enthusiasts alike delving into the elegant and abstract world of group theory. Duration - 3h 54m. Author - N.B. Singh. Narrator - Digital Voice Mary G. Published Date - Monday, 20 January 2025. Copyright - © 2024 N.B. Singh ©.
Language:
English
Preface
Duration:00:01:22
About This Book
Duration:00:00:34
Introduction to Group Theory
Duration:00:01:01
Definitions and Examples
Duration:00:04:19
Basic Properties of Groups
Duration:00:08:59
Finite and Infinite Groups
Duration:00:07:33
Symmetry and Permutation Groups
Duration:00:07:39
Matrix Groups
Duration:00:06:13
Dihedral Groups
Duration:00:05:58
Historical Background
Duration:00:06:22
Subgroups and Cyclic Groups
Duration:00:00:56
Subgroup Criteria
Duration:00:05:38
Examples of Subgroups
Duration:00:05:42
Cyclic Groups and Generators
Duration:00:04:15
Properties of Cyclic Groups
Duration:00:03:51
Order of an Element
Duration:00:03:27
Subgroups of Cyclic Groups
Duration:00:02:59
Applications of Cyclic Groups
Duration:00:04:20
Group Homomorphisms and Isomorphisms
Duration:00:01:05
Kernel and Image
Duration:00:05:42
Properties of Homomorphisms
Duration:00:05:59
The Isomorphism Theorems
Duration:00:05:39
Automorphisms
Duration:00:06:09
Endomorphisms
Duration:00:05:34
Applications of Homomorphisms
Duration:00:04:48
Cosets and Lagrange’s Theorem
Duration:00:01:00
Cosets and Their Properties
Duration:00:03:16
Lagrange’s Theorem
Duration:00:03:08
Applications of Lagrange’s Theorem
Duration:00:03:19
Index of a Subgroup
Duration:00:03:24
Normalizers and Centralizers
Duration:00:05:41
The Counting Principle
Duration:00:04:46
Applications in Symmetry
Duration:00:03:32
Normal Subgroups and Quotient Groups
Duration:00:01:00
Normal Subgroups: Definition and Examples
Duration:00:05:57
Properties of Normal Subgroups
Duration:00:06:57
Quotient Groups
Duration:00:03:16
The First Isomorphism Theorem
Duration:00:03:14
The Second and Third Isomorphism Theorems
Duration:00:03:21
The Correspondence Theorem
Duration:00:03:11
Applications of Quotient Groups
Duration:00:03:33
Group Actions and Sylow Theorems
Duration:00:01:05
Group Actions: Definition and Examples
Duration:00:03:59
Transitive Group Actions
Duration:00:03:43
The Orbit-Stabilizer Theorem
Duration:00:03:23
Applications of Group Actions
Duration:00:02:46
Sylow Theorems: Introduction
Duration:00:03:27
Proofs of Sylow Theorems
Duration:00:03:37
Applications of Sylow Theorems
Duration:00:03:08
Advanced Topics in Group Theory
Duration:00:01:08
Solvable and Nilpotent Groups
Duration:00:03:39
Free Groups
Duration:00:02:56
Group Presentations
Duration:00:02:57
Commutator Subgroups
Duration:00:04:56
Group Extensions
Duration:00:04:09
Simple Groups
Duration:00:03:47
Recent Developments in Group Theory
Duration:00:04:46