Group Theory NEP-2020 (BSC Second Year)
| University: | SRTMUN (Swami Ramanand Teerth Marathwada University Nanded) |
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| Course: | B.Sc. |
| Year/Semester: | 2nd Year - Third Semester |
| Duration: | 14 Months |
| Book Pages: | 220 |
| E-Book Price: |
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Group theory is a fundamental domain of abstract algebra that studies algebraic structures called groups. It provides a framework for analyzing mathematical structures with applications in algebra, number theory, geometry, cryptography, and physics.
This field emerged in the 19th century through Evariste Galois's work on polynomial equations and has evolved into a foundational mathematical discipline. This study examines core concepts, such as sets, binary operations, and groups, progressing to subgroups, cyclic groups, permutation groups, homomorphisms, and normal subgroups.
This material, supported by definitions, theorems, and proofs, serves undergraduate mathematics students and those interested in algebra, establishing a foundation for advanced studies in abstract algebra and its applications.
INDEX
Chapter 1: Introduction to Groups
1.1 Definition and Examples of Groups
1.2 Elementary Properties of Groups
1.3 Finite and Infinite Groups: Basic Differences
1.4 Subgroups and Their Classifications
1.5 Subgroup Tests: Two-Step and One-Step Methods
1.6 Centre of a Group: Concept and Applications
1.7 Centralizer of an Element in a Group
1.8 Group Tables and Symmetries (with examples)
Chapter 2: Cyclic and Permutation Groups
2.1 Definition and Properties of Cyclic Groups
2.2 Classification of Subgroups in Cyclic Groups
2.3 Generator of a Cyclic Group and Orders
2.4 Permutation Groups: Definition and Structure
2.5 Properties of Permutations and Cycle Notation
Chapter 3: Isomorphisms, Cosets, and Lagrange's Theorem
3.1 Isomorphisms: Definition and Illustrative Examples
3.2 Properties of Group Isomorphisms
3.3 Automorphisms and Inner Automorphisms
3.4 Cosets: Definition, Types, and Properties
3.5 Lagrange's Theorem: Statement and Proof
Chapter 4: Normal Subgroups and Homomorphisms
4.1 Normal Subgroups: Definition and Examples
4.2 Test for Normal Subgroups
4.3 Group Homomorphisms: Definition and Properties
4.4 Kernel and Image of a Homomorphism
4.5 Properties of Group Homomorphisms
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GROUP THEORY
Dr. Omprakash Kanoba Berdewad (M.Sc., B.Ed., Ph.D.)
Assistant Professor, Department of Mathematics
Digambarrao Bindu ACS College, Bhokar
Dist. Nanded-431801(MS) INDIA
Dr. Satish Bhaurao Chavhan (M.Sc., B.Ed., M.Phil., Ph.D.)
Assistant Professor & Head Department of Mathematics
Digambarrao Bindu ACS College, Bhokar
Dist. Nanded-431801(MS) INDIA
Paper back : ISBN 978-93-6342-048-9
eBook : ISBN 978-93-6342-763-1
Copyright @ Author 2025
First Editon: June 2025
Note: All rights reserved No part of this publication may be reproduced, distributed or transmitted in any form or by any means, including photocopying, recording, or other electronic or methods, without the written permission of the publisher and the Authors
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omkar45 21-Jul-2025 12:10 pm