GROUPS WITH RESTRICTIONS ON PROPER UNCOUNTABLE SUBGROUPS

被引：6
|
作者：
De Giovanni, Francesco [1 ,2 ]
Trombetti, Marco [1 ,2 ]
机构：
[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz, Complesso Univ Monte S Angelo,Via Cintia, Naples, Italy
[2] INdAM, GNSAGA, Rome, Italy
来源：
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA | 2019年 / 56卷 / 02期
关键词：
Uncountable group; metahamiltonian group; periodic subgroup;
D O I：
10.1556/012.2019.56.2.1427
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
A group G is called metahamiltonian if all its non-abelian subgroups are normal. The aim of this paper is to investigate the structure of uncountable groups of cardinality aleph in which all proper subgroups of cardinality aleph are metahamiltonian. It is proved that such a group is metahamiltonian, provided that it has no simple homomorphic images of cardinality aleph. Furthermore, the behaviour of elements of finite order in uncountable groups is studied in the second part of the paper.
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页码：154 / 165
页数：12
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