Normality in Uncountable Groups

Abstract

The main purpose of this paper is to describe the structure of uncountable groups of cardinality $\aleph$ in which all subgroups of cardinality $\aleph$ are normal. Moreover, uncountable groups are studied in which every uncountable non-abelian subgroup is normal.

Keywords

• uncountable group
• normal subgroup
• metahamiltonian group