SUBJECT
Title
Topics in group theory
Type of instruction
lecture + practical
Level
master
Faculty
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