Math 6320 Group theory


Group theory is a subject of central importance in algebra, has deep connections with many branches
of mathematics (including analysis, geometry and topology), and has become increasingly important in physics by providing a mathematical framework for the study of various kinds of symmetry. This course is intended for graduate students in mathematics, both pure and applied.


While preparing for the comprehensive exam in algebra, this course gives a general introduction to the theory
of (discrete) groups. The topics covered include action of groups on sets, Sylow theory, composition series and Jordan-Hoelder Theorem, solvable and nilpotent groups, free groups, presentation of a group by generators and relations, Cayley graphs and Nielsen-Schreier Theorem.


Undergraduate course of Abstract Algebra (such as MATH 3320); undergraduate Group Theory (such as MATH 4321) is recommended.


  • S. Lang. Algebra. Revised third ed. Graduate Texts in Mathematics,
    211. Springer-Verlag, New York, 2002.
  • J. Rotman. An introduction to the theory of groups. Fourth ed.
    Graduate Texts in Mathematics, 148. Springer-Verlag, New York, 1995.