# Mathematical Colloquium

### Friday, June 1, 2018, 2:15pm

Classification of groups of prime-power order

Bettina Eick (TU Braunschweig)

**Abstract: **

Groups are a mathematical formalisation of symmetries. The classification of groups of certain types is a central tool in understanding and analysing groups and their applications. A famous result in this direction is the classification of finite simple groups. This result was achieved by a collaborative effort of many mathematicians and it takes up more than 10,000 journal pages.

This talk considers a different type of finite group: the groups whose order is a prime-power. There are many deep and interesting results known on the classification of these groups, but a complete classification is not available. This talk gives a survey on the state of the art of the classification of groups of prime-power order.

Given a prime p and a natural number n, one can consider the function

f(p,n) of (isomorphism types of) groups of order p^n. The function f(p,n) can be considered as a function in p or as a function in n and then has different interesting asymptotic properties.

Further, using the order for the classification of groups of prime-power order is not the only way to approach this project. This talk considers other methods as well and discusses their results.

Wir laden herzlich alle Interessierten zu diesem Vortrag ein.

**Place: ** Hörsaal V Hauptgebäude, Templergraben 55, 52062 Aachen