Groups whose prime graph on class sizes has a cut vertex
| Autor: | Silvio Dolfi, Lucia Sanus, Emanuele Pacifici, Víctor Sotomayor |
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| Rok vydání: | 2021 |
| Předmět: |
Class (set theory)
Finite group General Mathematics Prime number Group Theory (math.GR) Vertex (geometry) Set (abstract data type) Combinatorics Conjugacy class Simple (abstract algebra) Prime graph FOS: Mathematics 20E45 Finite groups Conjugacy classes Prime graph Mathematics - Group Theory Mathematics |
| Zdroj: | Israel Journal of Mathematics. 244:775-805 |
| ISSN: | 1565-8511 0021-2172 |
| DOI: | 10.1007/s11856-021-2193-2 |
| Popis: | Let $G$ be a finite group, and let $\Delta(G)$ be the prime graph built on the set of conjugacy class sizes of $G$: this is the simple undirected graph whose vertices are the prime numbers dividing some conjugacy class size of $G$, two vertices $p$ and $q$ being adjacent if and only if $pq$ divides some conjugacy class size of $G$. In the present paper, we classify the finite groups $G$ for which $\Delta(G)$ has a cut vertex. |
| Databáze: | OpenAIRE |
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