# Intermediately fully invariant subgroup

From Groupprops

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

## Definition

### Symbol-free definition

A subgroup of a group is termed **intermediately fully characteristic** if it is fully characteristic in every intermediate subgroup of the group containing it.

### Definition with symbols

A subgroup of a group is termed **intermediately fully characteristic** in if, for any intermediate subgroup of , is fully characteristic in : for any endomorphism of , .