Ben Gurion University of the Negev
Department of Mathematics
Course number: 201.2.4201; Fall semester 2009/10
Lecturer: Yair Glasner, Office:Math building (58) room 205, e-mail: yairgl@math
Office hours: TBA,
Course hours
Sunday 16:10-18:00,
Wednesday 9:00-11:00.
Due March first to my mail box.
GRADING
The course grade will be given according to a few take home assignments to be given during the semmester.
Syllabus
- Solvable subgroups - the theorems of Zassenhaus, Jordan and Platonov,
- Local fields, the pro-finite topology, profinite and pro-p groups.
- Applications: residual finiteness and virtual torsion freeness for finitely generated groups in characteristic zero.
- Free groups and the Tits alternative.
- Zariski topology.
- Lattices and arithmetic groups.
- Strong approximation theorems: comparison between Zariski, pro-finite and congruence topologies.
RECOMMENDED BIBLIOGRAPHY:
- Raghunathan. Discrete subgroups of Lie groups, Ergebnisse der Mathematic, Springer Verlag, 1972. (especially chapter VIII).
- Wehrfritz. Infinite linear groups,. Ergebnisse der Mathematic, Springer Verlag, 1973.
- Dixon. Problems in group theory, Dover publications Inc, 1973 (especially chapter 10).
- Clifford. Representations induced in an invariant subgroup,Annals of mathematics 38 (1937) no. 3, pp. 533-550.
- Guivarc'h. Produits de matrices aleatoires et applications aux proprieties geometriques de sous-groups du groupe lineaire.Ergodic theory and dynamical systems 10 (1990) no. 3, pp. 438œôòô512.
- Tits. Free subgroups in linear groups. J. Algebra 20 (1972) pp. 250œôòô270.
- De la Harpe. Free groups in linear groups. Emseign. Math. (2) 29 (1983), no. 1-2, pp. 129œôòô144.
- Nikolov. Strong approximation methods in group theory, an LMS/EPSRC short course lecture notes. arXiv:0803.4165 math.GR.