C-groups of high rank for the symmetric groups

2015/10/30 by Fernandes, Maria Elisa, Leemans, Dimitri · 1 citation
#Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1510.08990

Abstract

We classify C-groups of ranks n-1 and n-2 for the symmetric group S_n. We also show that all these C-groups correspond to 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.

Cited by

• Testing chirality on hypertopes

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• String C-groups as transitive subgroups of Sym(n)
• Two gluing methods for string C-group representations of the symmetric groups
• The ranks of alternating string C-groups