Abstract Algebra I

Course content

Binary Operations, Groups, Subgroups, Subgroups generated by a set, Cyclic groups (generators and subgroups), Cosets and Lagrange?s Theorem. Normal Subgroups and Quotient groups, Homomorphisms and Isomorphisms, Permutation groups, Finite symmetric groups, Group actions, The orbit Stabilizer Theorem, Cayley?s Theorem, Conjugacy classes and the class equation, Cauchy?s theorem, Sylow theorems, Direct products, The fundamental theorem of finite abelian groups.