String C-group representations of alternating groups

DOI10.26493/1855-3974.1953.c53zbMath1433.52010arXiv1810.12450OpenAlexW2981996268WikidataQ126847281 ScholiaQ126847281MaRDI QIDQ5217074

Maria Elisa Fernandes, Dimitri Leemans

Publication date: 21 February 2020

Published in: Ars Mathematica Contemporanea (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.12450

zbMATH Keywords

Coxeter groupsalternating groupsabstract regular polytopesstring C-groups

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Simple groups: alternating groups and groups of Lie type (20D06)

Related Items (5)

A rank augmentation theorem for rank three string C-group representations of the symmetric groups ⋮ Rank reduction of string C-group representations ⋮ On the ranks of string C-group representations for symplectic and orthogonal groups ⋮ String C-group representations of almost simple groups: A survey ⋮ The Degrees of Regular Polytopes of Type [4, 4, 4]

Uses Software

• Magma

Cites Work

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• The intersection condition for regular polytopes
• Almost simple groups with socle PSL\((2,q)\) acting on abstract regular polytopes
• Three-dimensional classical groups acting on polytopes
• Polytopes of high rank for the alternating groups
• Polytopes of high rank for the symmetric groups
• An atlas of abstract regular polytopes for small groups
• String C-groups as transitive subgroups of \(\operatorname{S}_n\)
• A new Petrie-like construction for abstract polytopes
• The Magma algebra system. I: The user language
• Independent generating sets and geometries for symmetric groups
• The smallest regular polytopes of given rank
• Orthogonal groups in characteristic 2 acting on polytopes of high rank
• On regular polytopes of 2-power order
• Existence of regular 3-polytopes of order \(2^n\)
• CPR graphs and regular polytopes
• An atlas of small regular abstract polytopes
• All Alternating Groups $A_n$ with $n\geq12$ Have Polytopes of Rank $\lfloor\frac{n-1}{2}\rfloor$
• Almost simple groups of Suzuki type acting on polytopes
• Polytopes with groups of type PGL_2(q)
• Generators for Alternating and Symmetric Groups
• MORE ON GENERATORS FOR ALTERNATING AND SYMMETRIC GROUPS
• Abstract Regular Polytopes
• Groups of Ree type in characteristic 3 acting on polytopes
• An extension of the classification of high rank regular polytopes
• Rank reduction of string C-group representations
• Highest rank of a polytope for An
• PRIMITIVE PERMUTATION GROUPS CONTAINING A CYCLE
• ABSTRACT REGULAR POLYTOPES FOR THE O'NAN GROUP
• Groups of type L ₂(q) acting on polytopes
• Polytopes of large rank for \(\mathrm{PSL}(4,\mathbb{F}_q)\)

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