Polycharacteristic subgroup

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 defining ingredient::contranormal subgroup in the closure of $$H$$ in $$G$$ under the action of the cyclic subgroup generated by $$\sigma$$.

Stronger properties

 * Weaker than::Characteristic subgroup
 * Weaker than::Procharacteristic subgroup
 * Weaker than::Weakly procharacteristic subgroup
 * Weaker than::Paracharacteristic subgroup
 * Weaker than::Intermediately isomorph-conjugate subgroup
 * Weaker than::Intermediately automorph-conjugate subgroup

Weaker properties

 * Stronger than::Normal-to-characteristic subgroup

Facts

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