# Characteristic of CDIN implies CDIN

From Groupprops

This article describes a computation relating the result of the Composition operator (?) on two known subgroup properties (i.e., Characteristic subgroup (?) and CDIN-subgroup (?)), to another known subgroup property (i.e., CDIN-subgroup (?))

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This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., characteristic subgroup) must also satisfy the second subgroup property (i.e., left-transitively CDIN-subgroup)

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## Statement

### Statement with symbols

Suppose are groups such that is characteristic in and is a CDIN-subgroup of . Then is a CDIN-subgroup of .