On maximal cyclic subgroups in finite p-groups

被引：0

作者：

Janko, Zvonimir ^{[1
]}

机构：

[1] Univ Heidelberg, Math Inst, D-69120 Heidelberg, Germany

来源：

MATHEMATISCHE ZEITSCHRIFT | 2006年 / 254卷 / 01期

关键词：

finite p-groups; powerful p-groups; metacyclic p-groups;

D O I：

10.1007/s00209-005-0916-4

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this note we consider finite noncyclic p-groups G all of whose maximal cyclic subgroups X satisfy one of the following two properties. (a) If each subgroup H of G containing X properly is nonabelian, then p = 2 and G is generalized quaternion. (b) If X is contained in exactly one maximal subgroup of G, then G is metacyclic. This solves the problems Nr.1541 and Nr. 1594 from [1].

引用

页码：29 / 31

页数：3