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]
This article defines a term that has been used or referenced in a journal article or standard publication, but may not be generally accepted by the mathematical community as a standard term.[SHOW MORE]
A subgroup of a group is termed normality-small if the only normal subgroup with which its product is the whole group, is in fact the whole group.
Definition with symbols
In terms of the small operator
This property is obtained by applying the small operator to the property: normality
View other properties obtained by applying the small operator
The small operator takes as input a subgroup property and outputs the property of being a subgroup whose join with every proper subgroup having this property is proper. The subgroup property of being normality-small is obtained by applying the small operator to the subgroup property of normality.
Relation with other properties
This subgroup property is left-hereditary: any subgroup of a subgroup with this property also has this property. Hence, it is also a transitive subgroup property.
Any subgroup sitting inside a normality-small subgroup is normality-small. This follows directly from the definition.