MA2L305
Undergraduate (ITEP)
· Generally offered: Spring
Abstract Algebra
L 3 T 1 P 0 Credits 4 Hours 4
Unit I: Definition, examples and properties of groups, Subgroups, Normal Subgroups, Quotient groups,
Homomorphism, Isomorphism theorems, Order of a subgroup, Lagrange’s Theorem.
Unit II: Subgroups generated by subsets of a group, Cyclic group, Dihedral group, Group actions, Orbit - Stabilizer Theorem, Centralizer, Normalizer, Class Equation.
Unit III: Symmetric and Alternating groups, Simplicity of A_n, Cayley’s Theorem, Automorphism groups, Direct product.
Unit IV: The Sylow Theorems, Structure theorem of finite abelian groups. Introduction to rings and fields with examples.
Full syllabus document →
Unit II: Subgroups generated by subsets of a group, Cyclic group, Dihedral group, Group actions, Orbit - Stabilizer Theorem, Centralizer, Normalizer, Class Equation.
Unit III: Symmetric and Alternating groups, Simplicity of A_n, Cayley’s Theorem, Automorphism groups, Direct product.
Unit IV: The Sylow Theorems, Structure theorem of finite abelian groups. Introduction to rings and fields with examples.