discipline 
Pure
Mathematics

subject 
Elementary group theory and pgroups

lecturers 
Péter
Hermann, Péter
Pál Pálfy, József Pelikán 
credits 
2 
period 

curriculum 
Combinatorial
group theory: free groups; the NielsenSchreier
theorem, Schreier’s index formula, Cayley graphs of free groups. Solvable
groups: generalizations of Sylow’s theorems to Hall
subgroups, psolvability.
Applications of the transfer (Burnside’s theorem on the existence of normal pcomplements, Schur’s
theorem on finiteness of commutator subgroups
implied by the finite index of the centre). Basic commutators,
central series in pgroups. Regular
pgroups, pgroups 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 pgroups. Asymptotic group
theory. 
literature 
Robinson:
A Course in the Theory of Groups 
form of tuition 
Lecture 
mode of assessment 
written/oral
exam 