Strongly central series

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

View a complete list of properties of subgroup series

Definition

$G = K_{1} \geq K_{2} \geq K_{3} \geq \dots \geq K_{c} \geq K_{c + 1} = 1$

is termed strongly central if $[K_{i}, K_{j}] \leq K_{i + j}$ for every $i, j = 1, 2, \dots, c$ .

The lower central series and upper central series of a nilpotent group are both examples of strongly central series.