Utkal University, Odisha, Mathematics Semester 3, Group Theory-I Syllabus

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Unit - 1 Symmetries Of A Square

Unit 1

Symmetries of a square

1.1 Symmetries of a square

1.2 Dihedral groups

1.3 Definition and examples of groups including permutation groups and quaternion groups illustration through matrices

1.5 Elementary properties of groups

1.6 Subgroups and examples of subgroups

1.7 Centralizer normalizer and center of a group.

Unit - 2 Product Of Two Subgroups

Unit 2

Product of two subgroups

2.1 Product of two subgroups

2.2 Properties of cyclic groups

2.3 Classification of subgroups of cyclic groups

2.4 Cycle notation for permutations

2.5 Properties of permutations even and odd permutations

2.6 Alternating group

Unit - 3 Properties Of Cosets

Unit 3

Properties of cosets

3.1 Properties of cosets

3.2 Lagranges theorem and consequences including Fermats Little theorem

3.3 External direct product of a finite number of groups

3.4 Normal subgroups and factor groups

Unit - 4 Cauchy's Theorem For Finite Abelian Groups

Unit 4

Cauchys theorem for finite abelian groups

4.1 Cauchys theorem for finite abelian groups

4.2 Group homomorphisms properties of homomorphisms

4.3 Cayleys theorem

4.4 Properties of Isomorphisms

4.5 First second and third isomorphism theorems.

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Other Subjects of Semester-3
Theory of real functions
Partial differential equations and system of odes
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