Strongly central series

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This article defines a property that can be evaluated for a subgroup series


View a complete list of properties of subgroup series

Definition

A subgroup series

G = K_1 \ge K_2 \ge K_3 \ge \ldots \ge K_c \ge K_{c+1} = 1

is termed strongly central if [K_i,K_j] \le K_{i+j} for every i,j = 1,2,\ldots,c.

(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

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)