On the structure of some contranormal-free groups

Abstract

A subgroup H of a group G is contranormal if $H^G=G.$ In finite groups, if there are no proper contranormal subgroups, then the group is nilpotent but this is not true in infinite groups as the well-known Heineken–Mohamed groups show. We call such groups without proper contranormal subgroups “contranormal-free.” In this article, we prove various results concerning contranormal-free groups proving, for example that locally generalized radical contranormal-free groups which have finite section rank are hypercentral.

Keywords:

• Contanormal subgroup
• finitely generated group
• hypercentral group
• nilpotent group

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 20E15
• Secondary 20F16
• 20F22