Transfer condition operator

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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 property


View a complete list of subgroup property modifiers OR View a list of all subgroup property operators (possibly with multiple inputs)

Definition

Suppose p is a subgroup property. The transfer condition operator applied to p, denoted T(p), is defined as the following property: a subgroup H of a group G satisfies T(p) if, for any subgroup K of G, H \cap K satisfies property p in K.