discipline

Pure Mathematics

subject

Elementary group theory and p-groups

lecturers

Péter Hermann, Péter Pál Pálfy, József Pelikán

credits

2

period

 

curriculum

Combinatorial group theory: free groups; the Nielsen-Schreier theorem, Schreier’s index formula, Cayley graphs of free groups. Solvable groups: generalizations of Sylow’s theorems to Hall subgroups, p-solvability. Applications of the transfer (Burnside’s theorem on the existence of normal p-complements, Schur’s theorem on finiteness of commutator subgroups implied by the finite index of the centre). Basic commutators, central series in p-groups. Regular p-groups, p-groups of maximal class. Powerful groups: analogues to some properties of abelian (and regular) groups, the existence of large powerful subgroups in arbitrary groups. Linear methods in finite p-groups. Asymptotic group theory.

literature

Robinson: A Course in the Theory of Groups

form of tuition

Lecture

mode of assessment

written/oral exam