Editing Generating set of a group (section)

==Frattini subgroup==
An interesting companion topic is that of ''non-generators''. An element <math>x</math> of the group <math>G</math> is a non-generator if every set <math>S</math> containing <math>x</math> that generates <math>G</math>, still generates <math>G</math> when <math>x</math> is removed from <math>S</math>. In the integers with addition, the only non-generator is 0. The set of all non-generators forms a subgroup of <math>G</math>, the [[Frattini subgroup]].