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 characteristic satisfies the subgroup metaproperty of being transitive.

Verbal statement

A characteristic subgroup of a characteristic subgroup is characteristic in the whole group.

Symbolic statement

Let H be a characteristic subgroup of K, and K a characteristic subgroup of G. Then, H is a characteristic subgroup of G.

Proof

PLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]

References

Textbook references

  • Groups and representations by Jonathan Lazare Alperin and Rowen B. Bell, ISBN 0387945261More info, Page 17, Lemma 4
  • A Course in the Theory of Groups by Derek J. S. Robinson, ISBN 0387944613More info, Page 28, Characteristic and Fully invariant subgroups, 1.5.6(ii)