Left-inner subgroup property

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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


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

Relation with other metaproperties

Stronger metaproperties

Weaker metaproperties