Groups with restrictions on proper uncountable subgroups-Reference-Cited by-同舟云学术

Groups with restrictions on proper uncountable subgroups

Published:2019-06 Issue:2 Volume:56 Page:154-165
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
language:
Short-container-title:Studia Scientiarum Mathematicarum Hungarica

Author:

De Giovanni Francesco¹,Trombetti Marco¹

Affiliation:

1. 1Dipartimento di Matematica e Applicazioni, Università di Napoli Federico II, Complesso Universitario Monte S. Angelo, Via Cintia, Napoli, Italy

Abstract

Abstract 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 ℵ in which all proper subgroups of cardinality ℵ are metahamiltonian. It is proved that such a group is metahamiltonian, provided that it has no simple homomorphic images of cardinality ℵ. Furthermore, the behaviour of elements of finite order in uncountable groups is studied in the second part of the paper.

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Link

https://www.akademiai.com/doi/pdf/10.1556/012.2019.56.2.1427

Reference20 articles.

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