MTH423: Structure of finite groups

        [Cr:4, Lc:3, Tt:1, Lb:0]

Course Outline

• Sylow theory. Fitting subgroup F(G).
• Subnormal subgroups. Characteristic subgroups. Wielandt zipper lemma. Baers theorem on subgroups of F(G).
• Commutators; solvable and nilpotent groups. Schur multiplier.
• Semi-direct products; central products and wreath products.
• Automorphism group. Horosevskiis theorem on the orders of elements in Aut(G).
• Hall-subgroups. Schur-Zassenhaus Theorem.
• Coprime action. Fitting theorem.
• Transfer. Burnsides normal p-complement theorem. Focal subgroup.
• Frobenius actions.
• The Thompson subgroup.
• Burnsides paqb-theorem.
• Permutation groups. Simple groups.

Recommended Reading

• M. Aschbacher, Finite Group Theory. Cambridge Studies in Advanced Mathematics, Cambridge University Press, 2000.
• B. Huppert, Endliche Gruppen I. Grudlehren der mathematischen Wissenschaften, Volume 134. Springer 1967.
• Martin Isaacs,Finite Group Theory. Graduate Studies in Mathematics, Volume 92. American Mathematical Society. 2008.
• Derek J. S. Robinson, A Course in the Theory of Groups, GTM Vol. 80. Springer, 1996.
• Harvey E. Rose, A Course on Finite Groups, Universitext. Springer, 2009.
• Joseph J. Rotman, An Introduction to the Theory of Groups, Springer, 1995.
• Bertram A. F. Wehrfritz,A Second Course on Group Theory, World Scientific, 1999.