Groups in which the prime graph is a tree

Lucido, Maria Silvia

Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002), p. 131-148 / Harvested from Biblioteca Digitale Italiana di Matematica

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Abstract
Résumé

The prime graph $Γ (G)$ of a finite group $G$ is defined as follows: the set of vertices is $π (G)$ , the set of primes dividing the order of $G$ , and two vertices $p$ , $q$ are joined by an edge (we write $p \sim q$ ) if and only if there exists an element in $G$ of order $p q$ . We study the groups $G$ such that the prime graph $Γ (G)$ is a tree, proving that, in this case, $|π (G)| \leq 8$ .

Il «prime graph» $Γ (G)$ di un gruppo finito $G$ è definito nel modo seguente: l'insieme dei vertici è $π (G)$ , cioè l'insieme dei primi che dividono l'ordine del gruppo e due vertici $p$ , $q$ costituiscono un lato (e si indica $p \sim q$ ) se esiste un elemento in $G$ di ordine $p q$ . Si studiano i gruppi $G$ tali che il grafo $Γ (G)$ è un albero, dimostrando che, in questo caso, $|π (G)| \leq 8$ .

Publié le : 2002-02-01

MR 1881928 | Zbl 1097.20022

@article{BUMI_2002_8_5B_1_131_0,
     author = {Maria Silvia Lucido},
     title = {Groups in which the prime graph is a tree},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {5-A},
     year = {2002},
     pages = {131-148},
     zbl = {1097.20022},
     mrnumber = {1881928},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_2002_8_5B_1_131_0}
}

Lucido, Maria Silvia. Groups in which the prime graph is a tree. Bollettino dell'Unione Matematica Italiana, Tome 5-A (2002) pp. 131-148. http://gdmltest.u-ga.fr/item/BUMI_2002_8_5B_1_131_0/

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