Under r-generation conditions on commutator subsets in finite groups, [G,P] or G' has r-bounded rank, with p-solubility or extra conditions required.
Gorenstein, Finite Groups , Chelsea Publishing Company, New York, 1980
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Rank type conditions on commutators in finite groups
Under r-generation conditions on commutator subsets in finite groups, [G,P] or G' has r-bounded rank, with p-solubility or extra conditions required.