Procharacteristic subgroup

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BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

Definition with symbols

  • (Left-action convention): A subgroup H of a group G is termed procharacteristic in G if, for any automorphism \sigma of G, there exists g \in \langle H, \sigma(H) \rangle such that gHg^{-1} = \sigma(H).
  • (Right-action convention): A subgroup H of a group G is termed procharacteristic in G if, for any automorphism \sigma of G, there exists g \in \langle H, H^\sigma\rangle such that H^g = H^\sigma.

Relation with other properties

Stronger properties

Weaker properties

Facts