1-completed 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]


BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

Definition

Symbol-free definition

A subgroup of a group is said to be 1-completed if there is a single element outside the subgroup such that that element, along with the subgroup, generates the whole group.

Definition with symbols

A subgroup H of a group G is said to be 1-completed if there is an element x in G such that the subgroup generated by H and x is the whole of G.

Relation with other properties

Stronger properties

Weaker properties

Metaproperties

Upward-closedness

This subgroup property is upward-closed: if a subgroup satisfies the property in the whole group, every intermediate subgroup also satisfies the property in the whole group
View other upward-closed subgroup properties