SUBJECT

Title

Topics in group theory

Type of instruction

lecture + practical

Level

master

Part of degree program
Credits

3+3

Recommended in

Semesters 1-4

Typically offered in

Autumn/Spring semester

Course description

Permutation groups. Multiply transitive groups, Mathieu groups. Primitive permutation groups, the O’Nan-Scott Theorem.

Simple groups. Classical groups, groups of Lie type, sporadic groups.

Group extensions. Projective representations, the Schur multiplier.

p-groups. The Frattini subgroup. Special and extraspecial p-groups. Groups of maximal class.

Subgroup lattices. Theorems of Ore and Iwasawa.

Readings
  • D.J.S. Robinson: A course in the theory of groups, Springer, 1993
  • P.J. Cameron: Permutation groups, Cambridge University Press, 1999
  • B. Huppert, Endliche Gruppen I, Springer, 1967