GROUP THEORY-I
| Chapter | Title | Page Range |
|---|---|---|
| Chapter 1 | Basic Concepts of Group Theory - 1 ~PDF | 01-07 |
| Chapter 2 | Introduction to Groups ~PDF | 08-25 |
| Chapter 3 | Groups ~PDF | 26-55 |
| Chapter 4 | Finite Groups; Subgroups ~PDF | 56-92 |
| Chapter 5 | Cyclic Groups ~PDF | 93-113 |
| Chapter 6 | Permutation Groups~PDF | 114-143 |
| Chapter 7 | Isomorphisms ~PDF | 144-156 |
| Chapter 8 | Cosets and Lagrange's Theorem ~PDF | 157-175 |
| Chapter 9 | External Direct Products ~PDF | 176-194 |
| Chapter 10 | Normal Subgroups and Factor Groups ~PDF | 195-218 |
| Chapter 11 | Group Homomorphisms ~PDF | 219-242 |
| Answers | Answers to Selected Exercises ~PDF | 243-310 |
GROUP THEORY-I SYLLABUS
UNIT-I
Symmetries of a square, Dihedral groups, definition and examples of groups including permutation groups and quaternion groups (illustration through matrices), elementary properties of groups, Subgroups and examples of subgroups, centralizer, normalizer, center of a group,
UNIT-II
Product of two subgroups, Properties of cyclic groups, classification of subgroups of cyclic groups, Cycle notation for permutations, properties of permutations, even and odd permutations,alternating group,
UNIT-III
Properties of cosets, Lagrange's theorem and consequences including Fermat's Little theorem,external direct product of a finite number of groups, normal subgroups, factor groups.
UNIT-IV
Cauchy's theorem for finite abelian groups, group homomorphisms, properties of homomorphisms, Cayley's theorem, properties of isomorphisms, first, second and third isomorphism theorems.
