# Left-inner subgroup property

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
View a complete list of subgroup metaproperties
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

## Definition

### Symbol-free definition

A subgroup property is said to be left-inner if, in the function restriction formalism, it has a restriction formal expression with the left side being inner automorphisms.

### Definition with symbols

A subgroup property $p$ is said to be left-inner if, in the function restriction formalism, there exists a restriction formal expression for $p$ of the form:

Inner automorphism $\to b$

where $b$ is any function property.

In other words, a subgroup $H$ satisfies property $p$ in $G$ if and only if every inner automorphism on $G$ restricts to a function on the subgroup satisfying property $b$.

### In terms of the left expressibility operator

The subgroup metaproperty of being left-inner is obtained by applying the left expressibility operator to the function metaproperty of being exactly equal to the inner automorphism