# Derived length

From Groupprops

*This article defines an arithmetic function on a restricted class of groups, namely:* solvable groups

## Definition

### Symbol-free definition

Given a solvable group, we define its **solvable length** as follows: it is the length of the derived series of the group. Note here that by length of the series, we mean the number of successive inclusions, so the length is one less than the actual number of subgroups in the derived series.