Levi operator

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This article defines a group property modifier (a unary group property operator) -- viz an operator that takes as input a group property and outputs a group property

Definition

Symbol-free definition

The Levi operator is a map from the group property space to the group property space that takes as input a group property p and outputs the property of being a group where every point-closure (viz the normal closure of every element) satisfies the group property p as an abstract group.

Definition with symbols

The Levi operator is a map from the group property space to the group property space that takes as input a group property p and gives as output the property of being a group G such that for any element x in G, the normal closure of x satisfies property p as an abstract group.

Application

Important instances of application of the Levi operator: