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Syllabus

Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem. Rings, subrings and ideals, homomorphisms of rings; Integral domains, principal ideal domains, Euclidean domains and unique factorization domains; Fields, quotient fields.

 

Course Curriculum

Defining Groups 00:33:00
INTRODUCTION TO GROUP
Modulo Arithmetic 00:42:00
Cayley Table 00:12:00
Unit Group 00:12:00
Group of Matrices 00:22:00
Dihedral Groups 01:31:00
Subgroup 00:47:00
Problems on Groups 01:39:00
CYCLIC GROUP
Cyclic Groups 01:30:00
PERMUTATION GROUP
Permutation Group 01:57:00
ISOMORPHISM OF GROUPS
Isomorphism of Groups 02:17:00
EXTRNAL DIRECT PRODUCT
External Direct Product 00:51:00
HOMOMORPHISM OF GROUP
Homomorphism of Groups 04:12:00

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