Paranormal subgroup

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions

This is a variation of normality|Find other variations of normality | Read a survey article on varying normality

Definition

Definition with symbols

A subgroup $H$ of a group $G$ is termed paranormal if for any $g\in G$, there exists $x\in <H,H^{g}>$ such that $<H,H^{x}>=<H,H^{g}>$.

Relation with other properties

Stronger properties

• Normal subgroup
• Pronormal subgroup
• Abnormal subgroup

Weaker properties

• Polynormal subgroup