Coprime automorphism-faithful characteristicity is transitive

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This article gives the statement, and possibly proof, of a subgroup property satisfying a subgroup metaproperty
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Property "Page" (as page type) with input value "{{{metaproperty}}}" contains invalid characters or is incomplete and therefore can cause unexpected results during a query or annotation process.


Statement

Property-theoretic statement

The subgroup property of being a coprime automorphism-faithful characteristic subgroup satisfies the subgroup metaproperty of being transitive.

Statement with symbols

Suppose G is a finite group, K is a coprime automorphism-faithful characteristic subgroup of G, and H is a coprime automorphism-faithful characteristic subgroup of K. Then, H is a coprime automorphism-faithful characteristic subgroup of G.

Definitions used

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Proof

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