Utkal University, Odisha, Mathematics Semester 6, GROUP THEORY II Syllabus

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Unit - 1 Automorphism

Unit 1

Automorphism

1.1 Automorphism inner automorphism automorphism groups

1.2 Automorphism groups of finite and infinite cyclic groups applications of factor groups to automorphism groups 

1.3 Characteristic subgroups

Unit - 2 Commutator Subgroup And Its Properties

Unit 2

Commutator subgroup and its properties

2.1 Commutator subgroup and its properties

2.2 Properties of external direct products

2.3 The group of units modulo n as an external direct product

2.4 Internal direct products

2.5 Fundamental Theorem of finite abelian groups

Unit - 3 Group Actions

Unit 3

Group actions

3.1 Group actions

3.2 Stabilizers and kernels

3.3 Permutation representation associated with a given group action

3.4 Application of group actions Generalized Cayleys theorem Index theorem

Unit - 4 Groups Acting On Themselves By Conjugation

Unit 4

Groups acting on themselves by conjugation

4.1 Groups acting on themselves by conjugation

4.2 Class equation and consequences

4.3 Conjugacy in Sn p – groups

4.4 Sylows theorems and consequences

4.5 Cauchys theorem

4.6 Simplicity of An for n ≥ 5

4.7 Non simplicity tests

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Other Subjects of Semester-6
Number theory
Complex analysis
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