He entered the University of Rome in 1869, where he studied mathematics with Giuseppe Battaglini, Eugenio Beltrami, and Luigi Cremona, obtaining his PhD. in 1875.

In 1885 he published a paper where he defined a certain subgroup of a finite group. This subgroup, now known as the Frattini subgroup, is the subgroup Φ(G) generated by all the non-generators of the group G. He showed that Φ(G) is nilpotent and, in so doing, developed a method of proof known today as Frattini's argument.

References

• Search results an = (17.0097.01) at www.emis.de Giovanni Frattini, Intorno alla generazione dei gruppi di operazioni, Rom. Acc. L. Rend. (4) I. 281–285, 455–457, 1885.

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