Group Theory I & II: Course Outline (MAT 465) For Group Theory II
Course Objective
At the end of this course the students will be able to write mathematical proofs and reason of groups and introduction to representation theory. Tools which will be studied here would enable student to study complicated cases of Syllow’s group.
Course Contents
Actions of Groups, Permutation representation, Equivalence of actions, Regular representation, Cosets spaces, Linear groups and vector spaces, Affine groupa and affine spaces, Transitivity and orbits, Partition of Gspaces into orbits, Orbits as conjugacy class Computation of orbits, The classification of transitive Gspaces Catalogue of all transitive Gspaces up to Gisomorphism, Oneone correspondence between the right coset of Ga and the Gorbit, Gisomorphism between coset spaces and conjugation in G, Simplicity of A_5, FrobeniusBurnside lemma, Examples of morphisms, Ginvariance, Relationship between morphisms and congruences, Order preserving oneone correspondences between congruences on Ω and subrroups H of G that contain the stabilizer Gα, The alternating groups, Linear groups, Projective groups, Mobius groups, Orthogonal groups, unitary groups, Cauchy’s theorem, Pgroups, Sylow Psubgroups, Sylow theorems, Simplicity of An when n > 5.
Text Books

A first course in abstract algebra byCall Number: 512.02 FRAISBN: 9789332519039Publication Date: 2003