Topological Groups and Advanced Algebra

Code: MA722 | L-T-P-C: 4-0-0-8

MA722 Topological Groups and Advanced Algebra [4-0-0-8] Prerequisites: MA521 Modern Algebra.

Basic notions from point-set-topology, Direct product and inverse limits, Topological groups, completions, inverse system of finite groups, Profinite groups.

Nilpotent and Solvable groups, Frattini subgroups, Chief factors, Free groups, Presentations, Matrix groups and their properties, Profinite and Pro-p-groups.

The topology of pointwise convergence.

Texts:

1. I. D. Macdonalds, Theory of Groups, Oxford University Press, 1968
2. Dixon, Linear Groups, Dover
3. D. L. Johnson, Presentation of Groups, LMS series, CUP, 1990.
4. Dixon, Man, Segal, Analytic Pro-p Groups, LMS Series, Cambridge University Press
5. James R. Munkres, Topology: a first courses, Prentice-Hall, 1992.
6. P.J. Higgins, Introduction to topological groups, LMS Lecture series 15, CUP, 1974