6 ECTS credits
150 h study time
Offer 1 with catalog number 4013295FNR for all students in the 2nd semester at a (F) Master - specialised level.
1. Incidence geometry
- definitions
- morphisms and groups
- important examples
- subgeometries
2. Permutation groups
- definitions, actions, G-sets
- theorems on finite permutation groups
- primitive and quasiprimitive actions
- O'Nan--Scott type theorems
- applications
3. Geometries for groups
- coset geometries
- some examples and axioms
- diagram geometry
- the CFSG
- Tits Buildings
- incidence structures and quotients
P.J. Cameron, Projective and Polar Spaces, QMW Maths Notes 13, 1991.
D.E. Taylor, The Geometry of the Classical Groups, Sigma Series in Pure
Mathematics, Volume 9, Heldermann Verlag, Berlin, 1992.
J.D. Dixon and B. Mortimer, Permutation Groups, Springer Verlag, 1996.
A. Pasini, Diagram Geometries, Clarendon Press, 1995.
A.A. Ivanov and S. Shpectorov, Geometry of Sporadic Groups, Cambridge
University Press, 2002.
Peter J. Cameron, Permutation Groups, Cambridge University Press, 1998.
The student knows the basic concepts and theorems of incidence geometry.
The student knows the basic concepts and theorems of finite permutation group theory.
The student can work with geometric representations of groups.
The student is aware of the impact of incidence geometry on the theory of finite simple groups and permutation groups in general.
The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.
Within the Other Exam category, the following assignments need to be completed:
Permanent evaluation and homeworks. Oral presentation of an advanced topic.
This offer is part of the following study plans:
Master of Mathematics: Fundamental Mathematics (only offered in Dutch)