MATE-2101 Abstract Algebra I

Preliminary concepts: Sets and equivalency relations. Groups and subgroups: Binary operations, groups and subgroups, cyclic groups and generators. Groups and cosets: Permutation Groups, Orbits, Cycles and Alternating Groups, Introduction to Isomorphism and Cayley’s Theorem, Cosets and Lagrange’s Theorem, Direct Products and Finitely Generated Abelian Groups. Homomorphisms and Factor Groups: Homomorphisms, factor groups, simple groups, series of groups, action groups on sets, applications of G-sets in combinatorial analysis. Advanced Group Theory: Sylow’s Theorems, Free Abelian Groups, Free Groups. Rings and Fields: Rings, Fields and Integral Domains.