English

On chiral polytopes having a group PSL(3,q) as automorphism group

Group Theory 2020-05-13 v1 Combinatorics

Abstract

For each prime power q5q\geq 5, we construct a rank four chiral polytope that has a group PSL(3,q)PSL(3,q) as automorphism group and Schl\"afli type {q1,2(q1)(3,q1),q1}\{q-1,\frac{2(q-1)}{(3,q-1)},q-1\}. We also construct rank five polytopes for some values of qq and we show that there is no chiral polytope of rank at least six having a group PSL(3,q)PSL(3,q) or PSU(3,q)PSU(3,q) as automorphism group.

Keywords

Cite

@article{arxiv.2005.05746,
  title  = {On chiral polytopes having a group PSL(3,q) as automorphism group},
  author = {Dimitri Leemans and Adrien Vandenschrick},
  journal= {arXiv preprint arXiv:2005.05746},
  year   = {2020}
}