Groups Whose Proper Subgroups of Infinite Rank Have Polycyclic Conjugacy Classes

• 作者: Francesco de Giovanni Marco Trombetti
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 多环芳烃 共轭类 因子群 无穷秩 PC 无限秩 阿贝尔 基团
• 年，卷（期）: 2015,（2）
• 页码范围: 181-188
• 页数: 8页
• 分类号: O152.1
• 语种: 中文

摘要

A group G is called a PC-group if the factor group G/CG(〈X)^G) is polycyclic for each element x of G. It is proved here that if G is a group of infinite rank whose proper subgroups of infinite rank have the property PC, then G itself is a PC-group, provided that G has an abelian non-trivial homomorphic image. Moreover, under the same assumption, a complete classification of minimal non-PC groups is obtained.