Normal subgroup generated by a singleton subset

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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VIEW RELATED: Subgroup property implications | Subgroup property non-implications | Subgroup metaproperty satisfactions | Subgroup metaproperty dissatisfactions | Subgroup property satisfactions |Subgroup property dissatisfactions
VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

Definition

A subgroup of a group is termed a normal subgroup generated by a singleton subset if it is the normal subgroup generated by a subset of size one in it. (Note that this just says that there exists a subset of size one that generates it as a normal subgroup, not that every subset of size one in it generates it as a normal subgroup).