|
|||||
|
|
p-Groups with few conjugacy classes of normalizers |
|
| Authors: | Rolf Brandl Carmela Sica Maria Tota |
| Institution: | 1. Institut für Mathematik, Emil-Fischer-Stra?e 30, 97074, Würzburg, Germany 2. Departamento de Matemática, Universidade Federal da Bahia, Campus de Ondina, Av. Adhemar de Barros Ondina, 40170-110, Salvador, Bahia, Brasil 3. Dipartimento di Matematica, Università di Salerno, Via Ponte don Melillo, 84084, Fisciano (SA), Italy |
| Abstract: | For a group $G$ , denote by $\omega (G)$ the number of conjugacy classes of normalizers of subgroups of $G$ . Clearly, $\omega (G)=1$ if and only if $G$ is a Dedekind group. Hence if $G$ is a 2-group, then $G$ is nilpotent of class $\le 2$ and if $G$ is a $p$ -group, $p>2$ , then $G$ is abelian. We prove a generalization of this. Let $G$ be a finite $p$ -group with $\omega (G)\le p+1$ . If $p=2$ , then $G$ is of class $\le 3$ ; if $p>2$ , then $G$ is of class $\le 2$ . |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |