On numbers which are orders of nilpotent groups with bounded class

Abstract

Let $n$ be a positive integer. In this short note, we characterize those numbers $m$ for which any group of order $m$ is an $n$-Engel group and those numbers $m$ for which any group of order $m$ has all its subgroups subnormal of defect at most $n$.

Keywords

• engel group
• subnormal subgroup
• defect