Extensible implies subgroup-conjugating: Difference between revisions
(New page: {{automorphism property implication| stronger = extensible automorphism| weaker = subgroup-conjugating automorphism}} ==Statement== Every extensible automorphism of a group must ...) |
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# [[uses::Extensible implies permutation-extensible]] | # [[uses::Extensible implies permutation-extensible]] | ||
# [[uses:: | # [[uses::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== | ==Proof== | ||
The proof follows by piecing together facts (1) and (2). | The proof follows by piecing together facts (1) and (2). | ||
Latest revision as of 17:47, 7 April 2009
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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Get more facts about extensible automorphism|Get more facts about subgroup-conjugating automorphism
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
- Extensible implies permutation-extensible
- 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).