Stem extension: Difference between revisions
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* [[Schur covering group]] is a stem extension of maximal size. In the context of [[perfect group]]s, these are called [[universal central extension]]s. | * [[Schur covering group]] is a stem extension of maximal size. In the context of [[perfect group]]s, these are called [[universal central extension]]s. | ||
==Relation with other properties== | |||
===Weaker properties of group extensions=== | |||
* [[weak stem extension]] | |||
* [[central extension]] | |||
==Facts== | ==Facts== | ||
* [[Base of stem extension need not be the whole center]] | * [[Base of stem extension need not be the whole center]] | ||
Latest revision as of 19:41, 8 May 2013
Definition
A stem extension is a group extension where the base normal subgroup is contained in both the center and the derived subgroup of the whole group.
In particular, it is a special kind of 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.