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## Course Objectives:

The objective of the course is to introduce the fundamental theory of groups and their homomorphisms. Symmetric groups and group of symmetries are also studied in detail. Fermat’s Little theorem as a consequence of the Lagrange’s theorem on finite groups. Hence, Join The Best Online Math Tuition In Noida

## Course Learning Outcomes: The course will enable the students to:

i) Recognize the mathematical objects that are groups, and classify them as abelian, cyclic and permutation groups, etc;
ii) Link the fundamental concepts of Groups and symmetrical figures;
iii) Analyze the subgroups of cyclic groups;
iv) Explain the significance of the notion of cosets, normal subgroups, and factor groups.

## Groups and its Elementary Properties Tuition Class

Symmetries of a square, The Dihedral groups, Definition and examples of groups including permutation groups and quaternion groups (illustration through matrices), Elementary properties of groups. Hence, Groups and its Elementary Properties Tuition Class In Noida.

## Subgroups and Cyclic Groups Tuition Class

Subgroups and examples of subgroups, Centralizer, Normalizer, Center of a group, Product of two subgroups; Properties of cyclic groups, Classification of subgroups of cyclic groups. Hence, Subgroups and Cyclic Groups Tuition Class In Noida.

## Permutation Groups and Lagrange’s Theorem Tuition Class

Cycle notation for permutations, Properties of permutations, Even and odd permutations, alternating groups; Properties of cosets, Lagrange’s theorem and consequences including Fermat’s Little theorem; Normal subgroups, factor groups, Cauchy’s theorem for finite abelian groups. Hence, Permutation Groups and Lagrange’s Theorem Tuition Class In Noida.

## Group Homomorphisms Tuition Class

Group homomorphisms, Properties of homomorphisms, Group isomorphisms, Cayley’s theorem, Properties of isomorphisms, First, Second and Third isomorphism theorems for groups. Hence, Group Homomorphisms Tuition Class In Noida.