The Gruenberg-Kegel graph of finite solvable rational groups
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917626416988160 |
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| author | Debón, Sara C. García-Lucas, Diego del Río, Ángel |
| author_facet | Debón, Sara C. García-Lucas, Diego del Río, Ángel |
| contents | A finite group $G$ is said to be rational if every character of $G$ is rational-valued. The Gruenberg-Kegel graph of a finite group $G$ is the undirected graph whose vertices are the primes dividing the order of $G$ and the edges join different primes $p$ and $q$ whenever $G$ contains an element of order $pq$. In this paper, we complete the classification of the Gruenberg-Kegel graphs of finite solvable rational groups initiated in \cite{BKMdR}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_12883 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The Gruenberg-Kegel graph of finite solvable rational groups Debón, Sara C. García-Lucas, Diego del Río, Ángel Group Theory Representation Theory A finite group $G$ is said to be rational if every character of $G$ is rational-valued. The Gruenberg-Kegel graph of a finite group $G$ is the undirected graph whose vertices are the primes dividing the order of $G$ and the edges join different primes $p$ and $q$ whenever $G$ contains an element of order $pq$. In this paper, we complete the classification of the Gruenberg-Kegel graphs of finite solvable rational groups initiated in \cite{BKMdR}. |
| title | The Gruenberg-Kegel graph of finite solvable rational groups |
| topic | Group Theory Representation Theory |
| url | https://arxiv.org/abs/2306.12883 |