p-Groups with few conjugacy classes of normalizers

被引：0

作者：

Brandl, Rolf ^{[1
]}

Sica, Carmela ^{[2
]}

Tota, Maria ^{[3
]}

机构：

[1] Inst Math, D-97074 Wurzburg, Germany

[2] Univ Fed Bahia, Dept Matemat, BR-40170110 Salvador, BA, Brazil

[3] Univ Salerno, Dipartimento Matemat, I-84084 Fisciano, SA, Italy

来源：

MONATSHEFTE FUR MATHEMATIK | 2013年 / 172卷 / 02期

关键词：

Conjugacy classes; Normalizers; Finite p-groups; p-Groups of maximal class; NUMBER;

D O I：

10.1007/s00605-012-0473-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 <= 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) <= p + 1. If p = 2, then G is of class <= 3; if p < 2, then G is of class <= 2.

引用

页码：151 / 159

页数：9

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