# Left residual of 2-subnormal by normal is normal of characteristic

From Groupprops

Template:Left residual computation

This article gives a proof/explanation of the equivalence of multiple definitions for the term normal subgroup of characteristic subgroup

View a complete list of pages giving proofs of equivalence of definitions

## Statement

Suppose is a subgroup of a group . The following are equivalent:

- is a Normal subgroup of characteristic subgroup (?) of : in other words, there is a characteristic subgroup of such that is a normal subgroup of .
- Whenever is a Normal subgroup (?) of some group , is a 2-subnormal subgroup (?) of .