1. String C-groups of order $4p^m$
- Author
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Hou, Dong-Dong, Feng, Yan-Quan, Leemans, Dimitri, and Qu, Hai-Peng
- Subjects
Mathematics - Group Theory ,Mathematics - Combinatorics ,20B25, 20D10, 52B10, 52B15 - Abstract
Let $(G,\{\rho_0, \rho_1, \rho_2\})$ be a string C-group of order $4p^m$ with type $\{k_1, k_2\}$ for $m \geq 2$, $k_1, k_2\geq 3$ and $p$ be an odd prime. Let $P$ be a Sylow $p$-subgroup of $G$. We prove that $G \cong P \rtimes (\mathbb{Z}_2 \times \mathbb{Z}_2)$, $d(P)=2$, and up to duality, $p \mid k_1, 2p \mid k_2$. Moreover, we show that if $P$ is abelian, then $(G,\{\rho_0, \rho_1, \rho_2\})$ is tight and hence known. In the case where $P$ is nonabelian, we construct an infinite family of string C-group with type $\{p, 2p\}$ of order $4p^m$ where $m \geq 3$., Comment: arXiv admin note: text overlap with arXiv:2107.02925
- Published
- 2024