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arXiv · 2302.11943

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

Maria Elisa Fernandes·Claudio Alexandre Piedade·Olivia Reade
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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 $r\in\{4,5\}$ then $G\cong\PSL_2(11)$. 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.

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Maria Elisa Fernandes, Claudio Alexandre Piedade, Olivia Reade. 2023-02-23. String C-group representations of transitive Groups: a case study with degree $11$. https://arxiv.org/abs/2302.11943

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