# Frattini length

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

## Definition

### Symbol-free definition

Given a finite group, we define the **Frattini length** as follows: the length of the Frattini series. The Frattini series is the descending series corresponding to the Frattini subgroup, that is, it is obtained by iterating the subgroup-defining function namely the Frattini subgroup.