Paracharacteristic 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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RANDOM TIP:The metaproperties section lists important facts about the subgroup property, and addresses many of the natural questions that arise about it. It has links to proofs.

Definition

A subgroup H of a group G is termed paracharacteristic in G if for any automorphism σ of G, H is a contranormal subgroup of the subgroup \langle H, \sigma(H) \rangle.

Relation with other properties

Stronger properties

Weaker properties

Facts

Metaproperties

Trimness

This subgroup property is trim -- it is both trivially true (true for the trivial subgroup) and identity-true (true for a group as a subgroup of itself)
View all trim subgroup properties OR view trivially true subgroup properties OR view identity-true subgroup properties
Facts about Paracharacteristic subgroupRDF feed
Stronger thanParanormal subgroup  +, Polycharacteristic subgroup  +, Polynormal subgroup  +, and Normal-to-characteristic subgroup  +
Weaker thanIntermediately isomorph-conjugate subgroup  +, Procharacteristic subgroup  +, Characteristic subgroup  +, Abnormal subgroup  +, and Weakly abnormal subgroup  +
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