On groups with all proper subgroups finite-by-abelian-by-finite

被引：2
|
作者：
Dardano, Ulderico [1 ]
De Mari, Fausto [1 ]
机构：
[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Via Cintia Monte S Angelo, I-80126 Naples, Italy
来源：
ARCHIV DER MATHEMATIK | 2021年 / 116卷 / 06期
关键词：
Minimal-non-P; Core-finite; Commensurable; CN-subgroup; Infinite-rank;
D O I：
10.1007/s00013-021-01580-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that if all proper subgroups of a locally graded group G are finite-by-abelian-by-finite, then G contains a finite normal subgroup N such that all proper subgroups of G/N are abelian-by-finite. Then we apply this result to the study of groups which are minimal-non-P also for related group properties P. Finally we see how for locally (solubleby-finite) groups of infinite rank, it is enough to restrict attention to the proper subgroups with infinite rank.
引用
收藏
页码：611 / 619
页数：9
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