# Transfer condition operator

From Groupprops

This article defines a subgroup property modifier (a unary subgroup property operator) -- viz an operator that takes as input a subgroup property and outputs a subgroup propertyView a complete list of subgroup property modifiers OR View a list of all subgroup property operators (possibly with multiple inputs)

## Definition

Suppose is a subgroup property. The **transfer condition operator** applied to , denoted , is defined as the following property: a subgroup of a group satisfies if, for any subgroup of , satisfies property in .