FINITE GROUPS WITH MODULAR CHAINS

被引：3

作者：

Schmidt, Roland ^{[1
]}

机构：

[1] Univ Kiel, Math Seminar, D-24098 Kiel, Germany

来源：

COLLOQUIUM MATHEMATICUM | 2013年 / 131卷 / 02期

关键词：

finite group; subgroup lattice; nilpotent group; lower semimodular lattice; modular chain;

D O I：

10.4064/cm131-2-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In 1954, Kontorovich and Plotkin introduced the concept of a modular chain in a lattice to obtain a lattice-theoretic characterization of the class of torsion-free nilpotent groups. We determine the structure of finite groups with modular chains. It turns out that this class of groups lies strictly between the class of finite groups with lower semimodular subgroup lattice and the projective closure of the class of finite nilpotent groups.

引用

页码：195 / 208

页数：14