String C-group representations of transitive Groups: a case study with degree $11$
Group Theory
2023-11-02 v3
Abstract
In this paper we give a non-computer-assisted proof of the following result: if is an even transitive group of degree and has a string C-group representation with rank then . Moreover this string C-group is the group of automorphisms of the rank polytope known as the -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.
Keywords
Cite
@article{arxiv.2302.11943,
title = {String C-group representations of transitive Groups: a case study with degree $11$},
author = {Maria Elisa Fernandes and Claudio Alexandre Piedade and Olivia Reade},
journal= {arXiv preprint arXiv:2302.11943},
year = {2023}
}