# Left-inner right-monoidal subgroup property

From Groupprops

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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 metapropertyVIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

## Statement

A subgroup property is termed a **left-inner right-monoidal subgroup property** if it can be expressed using a function restriction expression of the form:

where is a monoidal function property -- in other words, for any group, the collection of functions from the group to itself satisfying property forms a monoid under composition.