Strongly central series
From Groupprops
This article defines a property that can be evaluated for a subgroup seriesView a complete list of properties of subgroup series
Contents
Definition
is termed strongly central if for every .
(A similar definition works for transfinite series).
Examples
The lower central series and upper central series of a nilpotent group are both examples of strongly central series. Further information: Lower central series is strongly central, Upper central series is strongly central
Relation with other properties
Weaker properties
- Normal series: For full proof, refer: Strongly central series implies normal series
- Central series: For full proof, refer: Strongly central series implies central series
References
Textbook references
- Nilpotent groups and their automorphisms by Evgenii I. Khukhro, ISBN 3110136724, ^{More info}, Page 76, Section 3.2 (formal definition, around equation 3.2.5)