Uncountable groups in which normality is a transitive relation
Abstract
A group is called a T-group if all its subnormal subgroups are normal. It is proved here that if G is an uncountable soluble periodic group of regular cardinality ℵ in which all subnormal subgroups of cardinality ℵ are normal, then G is a T-group, provided that it satisfies a suitable residual condition. An example shows that this latter restriction cannot be avoided.
Communicated by A. Ol’shanskii
Remember to check out the Most Cited Articles! |
---|
Check out Algebra & Computation books in the Mathematics 2021 catalogue. |