Lecture Notes on Group Theory 
BY  G Q Abbasi pdf

Table of contents 

Chapter 1 

Groups 

Algebraic structures 

Types of binary operations 

Groups 

How to construct a group 

Cyclic groups 

Abelian and non abelian groups 

Chapter 2 

Subgroups,  Cosets and Lagrang's theorem 

The necessary e and and sufficient conditions 

 subgroups of a cyclic group 

Cosets

Lagrange theorem and its applications 

Applications of Lagrange theorem's theorem

How to find /construct subgroups of a given group

subgroup of the general linear groups

Chapter 3 

Normalizer, centralizer, centre , Conjugancy classes 

Normalizer of subgroup 

centralizer  of a subgroup 

Centre of a group 

Conjugate and Conjugancy classes 

The class equation 

Conjugate subgroups 

Conjugate subgroups 

Normal subgroup 

Factor group 

How to find the factor group 

Chapter 4 

Isomorphism and order structure groups 

Isomorphism 

Application of isomorphism 

How to check isomorphism between groups 

Cayley's theorem 

Order structures of groups 

Isomorphism theorems

Applications 

Automorphism of groups 

How to find the Automorphism of group of a given group G 12 

Characteristic and fully invariant subgroups

Chapter 5 

Groups of permutations 

Permutations 

Cyclic permutations 

Action of permutations on mutually disjoint subsets 

Alternating group 'An; of degree 'n' 

Abelian subgroups of maximal order in 'An' ,Sn' 

Chapter 6 

Direct products of groups 

Definition and basic results 

Applications of direct product of groups 

Fundamental Theorem on finite abelian group 

Application of the Fundamental Theorem 

Semidirect product of groups 

How to construct a  semi direct product 

Relation to direct product 

Chapter 7 

Sylow'S theorems and their applications 

P-Group 

Cauchy's Lemma 

Sylow's theorem 

How to find Sylow's subgroup 

Application 

Some solved examples 

Chapter 8 

Series in groups solvable and super solvable groups 

Series in groups 

Schreier's theorem 

How to construct a normal series 

Ascending and descending series 

Composition / chief series 

Derived series and solvable Groups 

Finite solvable groups 

Super solvable series 

Converse to lagrange's theorem and super solvable groups 

Chapter 9 

Commentators and Nilpotent groups 

Commentators and Commentators calculus 

Nilpotent groups 

How to construct lower / upper Central series 

Some remarkable features of D(n), Q(n) and S(n) 

More about Nilopotent Groups 

The Frattini subgroups 

                                

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