Computational Group Theory with GAP
Bilbao 2018

The PhD course Computational Group Theory with GAP is organized by the University of the Basque Country. It will take place between Monday 29th January and Friday 9th February 2018.

Description of the course

Computational group theory is the study of groups by means of computers. It is concerned with designing and analysing algorithms and data structures to compute information about groups.

The course will cover some fundamentals of computational group theory.  We will take a look at how groups can be represented with a computer, along with some basic algorithms for computing properties of groups. The focus will be put on two classes of groups, namely, polycyclic groups and finitely presented groupsThe former represent a class of groups where algorithmic theory is well understood and properties can be efficiently computed. On the other hand, computation with finitely presented groups is far less efficient in general. Fundamental algorithms will be outlined.


Urban Jezernik (University of the Basque Country)
Primož Moravec (University of Ljubljana)


The course will take place at the Department of Mathematics at the UPV/EHU campus in Leioa. The lectures will take place from 11:30 to 13:00 and the lab sessions from 14:30 to 16:00. The lab sessions will be held at the Seminar room E.P1.22.

We expect that you bring your own laptop to the lab sessions. Try to install GAP in advance following these instructions.

Week 1

29/01 [classroom 0.13] Introductory class  GAP demo Lab session 1 Feedback
30/01 [classroom 0.27] Basics of pc groups GAP demo Lab session 2 
31/01 [classroom 0.27]  Presentations of fp groups GAP demo Lab session 3 
01/02 [classroom 0.7] Collection in pc groups GAP demo Lab session 4 
02/02 [classroom 0.27] Subgroups and quotients of fp groups GAP demo Lab session 5 

Week 2

05/02 [classroom 0.13] p-Series and p-Quotients  GAP demo Lab session 6
06/02 [classroom 0.27] Word problem in fp groups GAP demo Lab session 7 
07/02 [classroom 0.27]  p-Quotient algorithm GAP demo Lab session 8 
08/02 [classroom 0.7] Self similar groups  Lab session 9 
09/02 [classroom 0.27] p-Generation algorithm  Lab session 10Exam pdf 
Exam upload