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Course Contents

Groups, Examples and consequences, Subgroups, Subgroup lattice, Relation between groups, System of generators and relations in a group, Cyclic groups, Group and symmetries, Complexes and Coset decomposition of a group, Lagrange’s theorem, Normalizer and Centralizer, Conjugacy relation in a group, Normal Subgroups, Quotient groups, Group homomorphism, Kernel of homomorphism, Isomorphism theorems, Cayley’s theorem, Permutation groups, cyclic permutation, Order of a permutation, Even and odd permutation, Alternating group, Generators of the symmetric and Alternating groups.


Course Learning Outcomes

This Course focuses on basic topics in abstract algebra while introducing to students the language of advanced mathematics and techniques involved in proofs. It is expected that the students will understand and produce proofs. Once a student successfully completes the course, the student shall be ready to take other theoretical courses. This is the fundamental course in abstract algebra, the majority of follow up courses in both pure and applied mathematics assumes the material covered in this course.


subgroups theorem

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Discuss order of a group and order of elements with important results

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Introduction of groups and related examples

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Introduction of subgroups and their examples

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important Theorems regarding subgroups

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Theorems of subgroups

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subgroup Lattice

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group homomorphism

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cyclic group

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Theorem of cyclic group

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generators and relations

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generators in cyclic group

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Book Title : Topics in Algebra
Author : I. N. Herstein
Edition :
Publisher : Xerox Publishing Company



Book Title : A First Course in Abstract Algebra
Author : J. B. Fraleigh
Edition :
Publisher : Addison-Wesley Publishing Company, 2002.







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