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From Groupprops

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 SUBGROUP PROPERTY: Hall subgroup: A subgroup of a finite group whose order and index are relatively prime. Sylow subgroups are a special case.

Contents 1 Definition 1.1 Symbol-free definition 2 Relation with other properties 2.1 Stronger properties 2.2 Weaker properties

Definition

Symbol-free definition

A subgroup of a group is termed 2-hypernormalized if its normalizer is a normal subgroup.

Relation with other properties

Stronger properties

• Normal subgroup

Weaker properties

• Finitarily hypernormalized subgroup
• 2-subnormal subgroup
• Hypernormalized subgroup
• Subnormal subgroup
• Conjugate-permutable subgroup