Meta 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

Property-theoretic definition

The meta operator is a map from the group property space to itself, that takes as input a group property p and outputs the square of p under the group extension operator.

Definition with symbols

The meta operator is a map from the group property space to itself defined as follows: it takes as input a group property p and outputs the group property q defined as follows:

A group G has property q if there is a normal subgroup N \triangleleft G such that N and G/N both have property p (as abstract groups).

Application

Important instances of application of the meta operator: