## Abstract

We prove that the highest rank of a string C-group constructed from an alternating group

*A*_{n}is 3 if n=5, 4 if n=9, 5 if n=10, 6 if n=11, and ⌊(n−1)/2⌋ if n⩾12. Moreover, if n=3,4,6,7, or 8, the group*A*_{n}is not a string C-group. This solves a conjecture made by the last three authors in 2012.Original language | English |
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Pages (from-to) | 135-176 |

Number of pages | 42 |

Journal | Proceedings of the London Mathematical Society |

Volume | 115 |

Issue number | 1 |

Early online date | 28 Apr 2017 |

DOIs | |

Publication status | Published - 4 Jul 2017 |

## Keywords

- Abstract regular polytypes
- String C-groups
- Alternating groups
- Permutation groups

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