Sui gruppi finiti col rango di Cipolla uguale a uno

Zappa, Guido

Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 9 (1998) no. 2, pp. 81-88

Résumé

Let \( G \) be a non-abelian finite group, and \( Z \) be its center. Let \( I \) be the poset of centralizers of elements in \(G \setminus Z\). \( G \) is said to have «rank 1» if the lenght of \( I \) is \( 0 \), and is said to be an «\( \mathcal{M} \)-group» if every \( H \in I \) is abelian. Every \( \mathcal{M} \)-group has rank \( 1 \). Schmidt [10] classified the \( \mathcal{M} \)-groups. In this Note the rank 1 groups which are not \( \mathcal{M} \)-groups are classified.