Coprime automorphism-invariant normal subgroup: Difference between revisions
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* [[Coprime automorphism-invariant normal of normal Hall implies normal]] | * [[Coprime automorphism-invariant normal of normal Hall implies normal]] | ||
* [[Left residual of normal by normal Hall is coprime automorphism-invariant normal]] | * [[Left residual of normal by normal Hall is coprime automorphism-invariant normal]] | ||
* [[Hall-relatively weakly closed implies coprime automorphism-invariant normal]] | |||
Latest revision as of 15:36, 8 August 2009
This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: coprime automorphism-invariant subgroup and normal subgroup
View other subgroup property conjunctions | view all subgroup properties
Definition
A subgroup of a finite group is termed a coprime automorphism-invariant normal subgroup if it is both normal and coprime automorphism-invariant: it is invariant under all coprime automorphisms of the whole group.
Relation with other properties
Stronger properties
Weaker properties
Facts
- Coprime automorphism-invariant normal subgroup of Hall subgroup is normalizer-relatively normal
- Coprime automorphism-invariant normal of normal Hall implies normal
- Left residual of normal by normal Hall is coprime automorphism-invariant normal
- Hall-relatively weakly closed implies coprime automorphism-invariant normal