Conjecture that every characteristic subring of nilpotent Lie ring is powering-invariant

This article is about a conjecture. View all conjectures and open problems

Statement

This is a conjecture. It has not been proved and it may well be false.

The conjecture has the following equivalent formulations:

1. In a nilpotent Lie ring, every characteristic Lie subring (i.e., characteristic subgring of nilpotent Lie ring) is a powering-invariant Lie subring (i.e., powering-invariant subring of nilpotent Lie ring).
2. Every nilpotent Lie ring is a Lie ring in which every characteristic subring is powering-invariant.

Related conjectures

• Conjecture that every characteristic subgroup of nilpotent group is powering-invariant: These conjectures are partly related via the Lazard correspondence.

Partial truth

Truth based on ambient group

• Characteristic subgroup of abelian group implies powering-invariant settles the abelian Lie ring case.

Truth based on nature of characteristic subgroup

• Upper central series members are powering-invariant in Lie ring
• Lower central series members are powering-invariant in nilpotent Lie ring
• Derived series members are powering-invariant in nilpotent Lie ring