Polycharacteristic 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, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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Definition

A subgroup $H$ of a group $G$ is termed polycharacteristic in $G$ if the following holds: for any automorphism $\sigma$ of $G$, $H$ is a contranormal subgroup in the closure of $H$ in $G$ under the action of the cyclic subgroup generated by $\sigma$.

Relation with other properties

Stronger properties

• Characteristic subgroup
• Procharacteristic subgroup
• Weakly procharacteristic subgroup
• Paracharacteristic subgroup
• Intermediately isomorph-conjugate subgroup
• Intermediately automorph-conjugate subgroup

Weaker properties

• Normal-to-characteristic subgroup

Facts

• Polycharacteristic of normal implies polynormal
• Left residual of polynormal by normal equals polycharacteristic

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).
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