# Frattini subgroup is finitely generated implies subset is generating set iff image in Frattini quotient is

From Groupprops

## Statement

### Statement with symbols

Suppose is a group, and (the Frattini subgroup of ) is a finitely generated group. Then, a subset of is a generating set for if and only if the image of in the Frattini quotient under the quotient map, generates .