String C-group representations of transitive groups: a case study with degree 11

Fernandes, Maria Elisa; Piedade, Claudio Alexandre and Reade, Olivia (2024). String C-group representations of transitive groups: a case study with degree 11. The Art of Discrete and Applied Mathematics, 7(2), article no. 07.

DOI: https://doi.org/10.26493/2590-9770.1627.77a

Abstract

In this paper we give a non-computer-assisted proof of the following result: if G is an even transitive group of degree 11 and has a string C-group representation with rank r ∈  then G ≅ PSL2(11). Moreover this string C-group is the group of automorphisms of the rank 4 polytope known as the 11-cell.

The insights gained from this case study include techniques and observations concerning permutation representation graphs of string C-groups. The foundational lemmas yield a natural and intuitive understanding of these groups. These and similar approaches can be replicated and are applicable to the study of other transitive groups.

Viewing alternatives

Metrics

Item Actions

Export

You can export this page using these formats Digital Object Identifier - DOI