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Groups of Ree type in characteristic 3 acting on polytopes

(2018) ARS MATHEMATICA CONTEMPORANEA. 14(2). p.209-226
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Organization
Abstract
Every Ree group R(q), with q not equal 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.
Keywords
Abstract regular polytopes, string C-groups, small Ree groups, permutation groups

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Citation

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Chicago
Leemans, Dimitri, Egon Schulte, and Hendrik Van Maldeghem. 2018. “Groups of Ree Type in Characteristic 3 Acting on Polytopes.” Ars Mathematica Contemporanea 14 (2): 209–226.
APA
Leemans, D., Schulte, E., & Van Maldeghem, H. (2018). Groups of Ree type in characteristic 3 acting on polytopes. ARS MATHEMATICA CONTEMPORANEA, 14(2), 209–226.
Vancouver
1.
Leemans D, Schulte E, Van Maldeghem H. Groups of Ree type in characteristic 3 acting on polytopes. ARS MATHEMATICA CONTEMPORANEA. 2018;14(2):209–26.
MLA
Leemans, Dimitri, Egon Schulte, and Hendrik Van Maldeghem. “Groups of Ree Type in Characteristic 3 Acting on Polytopes.” ARS MATHEMATICA CONTEMPORANEA 14.2 (2018): 209–226. Print.
@article{8613734,
  abstract     = {Every Ree group R(q), with q not equal 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) {\textlangle} G {\textlangle}= Aut(R(q)) is not a C-group and therefore not the automorphism group of an abstract regular polytope of any rank.},
  author       = {Leemans, Dimitri and Schulte, Egon and Van Maldeghem, Hendrik},
  issn         = {1855-3966},
  journal      = {ARS MATHEMATICA CONTEMPORANEA},
  language     = {eng},
  number       = {2},
  pages        = {209--226},
  title        = {Groups of Ree type in characteristic 3 acting on polytopes},
  volume       = {14},
  year         = {2018},
}

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