English

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 GG is an even transitive group of degree 1111 and has a string C-group representation with rank r{4,5}r\in\{4,5\} then G\PSL2(11)G\cong\PSL_2(11). Moreover this string C-group is the group of automorphisms of the rank 44 polytope known as the 1111-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}
}
R2 v1 2026-06-28T08:47:46.848Z