Stem extension

Definition
A stem extension is a defining ingredient::group extension where the base normal subgroup is contained in both the defining ingredient::center and the defining ingredient::derived subgroup of the whole group.

In particular, it is a special kind of defining ingredient::central extension.

Related notions

 * Schur covering group is a stem extension of maximal size. In the context of perfect groups, these are called universal central extensions.

Weaker properties of group extensions

 * weak stem extension
 * central extension

Facts

 * Base of stem extension need not be the whole center