Two infinite families of chiral polytopes of type {4,4,4} with solvable automorphism groups
| Autor: | Dong-Dong Hou, Yan-Quan Feng, Marston Conder |
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| Rok vydání: | 2021 |
| Předmět: |
Algebra and Number Theory
010102 general mathematics Polytope 52B15 05E18 20B25 06A11 Type (model theory) Automorphism 01 natural sciences Combinatorics Integer Solvable group 0103 physical sciences FOS: Mathematics Mathematics - Combinatorics Order (group theory) Combinatorics (math.CO) 010307 mathematical physics 0101 mathematics Mathematics |
| Zdroj: | Journal of Algebra. 569:713-722 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2020.11.002 |
| Popis: | We construct two infinite families of locally toroidal chiral polytopes of type $\{4,4,4\}$, with $1024m^2$ and $2048m^2$ automorphisms for every positive integer $m$, respectively. The automorphism groups of these polytopes are solvable groups, and when $m$ is a power of $2$, they provide examples with automorphism groups of order $2^n$ where $n$ can be any integer greater than $9$. (On the other hand, no chiral polytopes of type $[4,4,4]$ exist for $n \leq 9$.) In particular, our two families give a partial answer to a problem proposed by Schulte and Weiss in [Problems on polytopes, their groups, and realizations, {\em Periodica Math.\ Hungarica\} 53 (2006), 231-255]. 10pages |
| Databáze: | OpenAIRE |
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