Direct product of groups (External and Internal). Isomorphism theorems - Diamond isomorphism theorem, Butterfly Lemma, Conjugate classes, Sylows theorm, p- sylow theorem .
Commutators, Derived subgroups, Normal series and Solvable groups, Composition series, Refinement theorem and Jordan-Holder theorem for infinite groups.
Polynomial rings, Euclidean rings. Modules, Submodules, Quotient modules Direct sums and Module Homomorphisms. Generation of modules, Cyclic modules.
Field theory - Extension fields, Algebraic and Transcendental extensions, Separable and inseparable extensions, Normal extensions. Splitting fields. Galois theory - the elements of Galois theory, Fundamental theorem of Galois theory,
Galois theory - the elements of Galois theory, Fundamental theorem of Galois theory , Solvalibility by radicals.