Frattini length

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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.