Extensible implies subgroup-conjugating

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

Statement

Every extensible automorphism of a group must be a subgroup-conjugating automorphism: it must sned every subgroup to a conjugate subgroup.

Related facts

Corollaries

Facts used

  1. Extensible implies permutation-extensible
  2. Equivalence of definitions of subgroup-conjugating automorphism: This essentially shows that the notion of permutation-extensible is equivalent to the notion of subgroup-conjugating.

Proof

The proof follows by piecing together facts (1) and (2).

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Facts about Extensible implies subgroup-conjugatingRDF feed
Fact aboutExtensible automorphism  +, and Subgroup-conjugating automorphism  +
Page classFact  +
Proves property satisfaction ofSubgroup-conjugating automorphism  +
UsesExtensible implies permutation-extensible  +, and Equivalence of definitions of subgroup-conjugating automorphism  +
Uses property satisfaction ofExtensible automorphism  +
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