For a group G, denote by ω(G) the number of conjugacy classes of normalizers of subgroups of G. Clearly, ω(G) = 1 if and only if G is a Dedekind group. Hence if G is a 2-group, then G is nilpotent of class ≤ 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 ω(G) ≤ p + 1. If p = 2, then G is of class ≤ 3; if p > 2, then G is of class ≤ 2.
p-Groups with few Conjugacy Classes of Normalizers
SICA, Carmela;TOTA, Maria
2013
Abstract
For a group G, denote by ω(G) the number of conjugacy classes of normalizers of subgroups of G. Clearly, ω(G) = 1 if and only if G is a Dedekind group. Hence if G is a 2-group, then G is nilpotent of class ≤ 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 ω(G) ≤ p + 1. If p = 2, then G is of class ≤ 3; if p > 2, then G is of class ≤ 2.File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
p-Groups with few Conjugacy Classes of Normalizers.pdf
accesso aperto
Tipologia:
Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza:
Creative commons
Dimensione
246.35 kB
Formato
Adobe PDF
|
246.35 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
