C-groups of high rank for the symmetric groups

JOURNAL OF ALGEBRA

卷:508

Article

Fernandes, Maria Elisa¹  Leemans, Dimitri^2,3 

[1] Univ Aveiro, Dept Math, Ctr Res & Dev Math & Applicat, Aveiro, Portugal

[2] Univ Auckland, Dept Math, Private Bag 92019, Auckland 1142, New Zealand

[3] Univ Libre Bruxelles, Dept Math, CP 216 Algebra & Combinatoire,Blvd Triomphe, B-1050 Brussels, Belgium

关键词: C-groups;    Regularity;    Thin geometries;    Abstract polytopes;    Hypertopes;    Coxeter groups;    Independent generating sets;    Inductively minimal geometries;   

DOI  :  10.1016/j.jalgebra.2018.04.031

来源: Elsevier

【 摘 要 】

We give presentations for the C-groups of rank n - 1 of the symmetric group S-n. We also classify C-groups of rank n - 2 for S-n, We show that all these C-groups correspond to regular hypertopes, that is, thin, residually connected flag transitive geometries. Therefore we generalise some similar results obtained in the framework of string C-groups that are in one-to-one correspondence with abstract regular polytopes. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free