Page 27 - DMTH403_ABSTRACT_ALGEBRA

Abstract Algebra Richa Nandra, Lovely Professional University

Notes Unit 2: Groups

CONTENTS
Objectives

Introduction
2.1 Binary Operations
2.1.1 Operation ’.’ Table
2.2 Group
2.2.1 Abelian Group

2.3 Properties of Groups
2.4 Different Types of Group
2.4.1 Integers Modulo n

2.4.2 The Symmetric Group
2.4.3 Complex Numbers
2.5 Summary
2.6 Keywords
2.7 Review Questions

2.8 Further Readings

Objectives

After studying this unit, you will be able to:

Discuss the binary operations

Explain the term abelian and non-abelian groups

Describe the cancellation laws and laws of indices for various groups

Discuss the properties of integers modulo n, permutations and complex numbers

Introduction

The theory of groups is one of the oldest branches of abstract algebra. It has many applications
in mathematics and in the other sciences. Group theory has helped in developing physics,
chemistry and computer science. Its own roots go back to the work of the eighteenth century
mathematicians Lagrange, Ruffini and Galois.
In this unit, we will study about the group theory in detail. We surge fine groups and give some
examples. After that we understand details of some properties of groups that the elements of a
group satisfy. Let us discuss all these one by one.

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