GROUPS WITH FEW NON-NORMAL SUBGROUPS
GROUPS WITH FEW NON-NORMAL SUBGROUPS
复制标题
DOI：
10.1142/9789812708670_0005
复制
发表时间：
2007-10
期刊：
影响因子：
--
通讯作者：
M. Falco;F. Giovanni;C. Musella
中科院分区：
文献类型：
--
作者：
M. Falco;F. Giovanni;C. Musella
Hekster 和 Lenstra [5] 描述了具有有限个非正规子群的无限群的结构，而非正规子群为多循环的群已在 [2] 中完全表征。在本文中，考虑具有有限多个既不是正规的也不是多循环的子群的群。特别地，证明了在具有该性质的任何局部分级非周期群中，所有非正规子群都是多循环的，并给出了这种类型的周期局部分级群的完整描述。
The structure of infinite groups with finitely many non-normal subgroups has been described by Hekster and Lenstra [5], while groups whose non-normal subgroups are polycyclic have been completely characterized in [2]. In this paper, groups with finitely many subgroups which are neither normal nor polycyclic are considered. In particular, it is proved that in any locally graded non-periodic group with this property all non-normal subgroups are polycyclic, and a full description of periodic locally graded groups of this type is given.