Fundamental concepts of infinite group theory, series of subgroups, radicals and residuals, finiteness conditions: finitely generated and finitely presented groups, groups with finite rank, periodic and locally finite groups, maximal and minimal conditions. Solvable and nilpotent groups, properties of upper and lower central series, residually finite groups, generalized nilpotent groups, Engel groups, local theorems and generalized solvable groups.

Detailed Information can be found on the Homepage of the Seminar/Proseminar on Group Theory.

Literatur

Textbook: Finiteness conditions and Generalized Solvable groups, Derek Robinson

Zusätzliche Informationen

Course language: English

Participants should feel comfortable with the contents of 'Linear algebra 1', and perhaps 'Linear algebra 2'. If there are interested students who have already done the 'Algebra und Zahlentheorie' module, we will also be able to find interesting topics for them.