Groups of Ree type in characteristic 3 acting on polytopes

Authors

  • Dimitri Leemans Université Libre de Bruxelles, Belgium
  • Egon Schulte Northeastern University, United States
  • Hendrik Van Maldeghem Universiteit Gent, Belgium

DOI:

https://doi.org/10.26493/1855-3974.1193.0fa

Keywords:

Abstract regular polytopes, string C-groups, small Ree groups, permutation groups

Abstract

Every Ree group R(q), with q ≠ 3 an odd power of 3, is the automorphism group of an abstract regular polytope, and any such polytope is necessarily a regular polyhedron (a map on a surface). However, an almost simple group G with R(q) < G ≤ Aut(R(q)) is not a C-group and therefore not the automorphism group of an abstract regular polytope of any rank.

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Published

2017-09-04

Issue

Vol. 14 No. 2 (2018)

Section

Articles

License

Articles in this journal are published under Creative Commons Attribution 4.0 International License
https://creativecommons.org/licenses/by/4.0/