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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