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.
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页码：151 / 159
页数：9
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