Procharacteristic subgroup
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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof.
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Definition
Definition with symbols
- (Left-action convention): A subgroup H of a group G is termed procharacteristic in G if, for any automorphism σ of G, there exists
such that gHg − 1 = σ(H).
- (Right-action convention): A subgroup H of a group G is termed procharacteristic in G if, for any automorphism σ of G, there exists
such that Hg = Hσ.
Relation with other properties
Stronger properties
Weaker properties
Facts