Pure PGR Seminar - Generators of crystallographic groups, Hollis (Southampton) Seminar

Event details

An n-dimensional crystallographic group is a discrete subgroup of the isometry group of the n-dimensional Euclidean space Rn with a compact orbit space. There is a conjecture said that if the group is torsion free, then the minimal number of generator is bounded by its dimension. In this talk, I will show that an n-dimensional crystallographic group with an odd prime p-group to be its holonomy group can be generated by n elements by considering the lattice part of the group as a module while the action is given by the holonomy group.