Infinite minimal non-hypercyclic groups

被引：30
作者：
de Giovanni, Francesco [1 ]
Trombetti, Marco [1 ]
机构：
[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz, I-80126 Naples, Italy
来源：
JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2015年 / 14卷 / 10期
关键词：
Minimal non-hypercyclic group; minimal non-hypercentral group; PROPER SUBGROUPS; RANK;
D O I：
10.1142/S0219498815501431
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
If X is a class of groups, a group G is minimal non-X if it is not an X-group, but all its proper subgroups belong to X. The aim of this paper is to prove that for an infinite locally graded group, the property of being minimal non-hypercentral and that of being minimal non-hypercyclic are equivalent. Moreover, the main properties of infinite minimal non-hypercentral groups are described. In the last section, we study groups of infinite rank in which all proper subgroups of infinite rank satisfy a generalized supersolubility condition.
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页数：15
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