CDIN of conjugacy-closed implies CDIN

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This article describes a computation relating the result of the Composition operator (?) on two known subgroup properties (i.e., CDIN-subgroup (?) and Conjugacy-closed subgroup (?)), to another known subgroup property
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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., conjugacy-closed subgroup) must also satisfy the second subgroup property (i.e., right-transitively CDIN-subgroup)
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Statement

Statement with symbols

Suppose H \le K \le G are groups such that H is a CDIN-subgroup of K and K is a conjugacy-closed subgroup of G. Then H is a CDIN-subgroup of G.

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