On numbers which are orders of nilpotent groups with bounded class

نویسندگان
Tortora, Antonio ID 1
Ferrara, Maria ID 2
Tota, Maria ID 3

1 Dipartimento di Matematica e Fisica, Università della Campania “Luigi Vanvitelli”, viale Lincoln, 5 - 81100, Italy

2 Dipartimento di Matematica e Fisica, Università della Campania “Luigi Vanvitelli”, viale Lincoln, 5 - 81100, Italy

3 Dipartimento di Matematica, Università di Salerno, via Giovanni Paolo II, 132 - 84084 - Fisciano (SA), Italy

doi
10.22108/ijgt.2023.137950.1851
چکیده

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 $n$.

کلیدواژه‌ها
Engel group, subnormal subgroup, defect