Giovanni Frattini

Giovanni Frattini (8 January 1852 – 21 July 1925) was an Italian mathematician, noted for his contributions to group theory.

Biography
Frattini entered the University of Rome in 1869, where he studied mathematics with Giuseppe Battaglini, Eugenio Beltrami, and Luigi Cremona, obtaining his Laurea 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 $$\Phi(G)$$ generated by all the non-generators of the group $$G$$. He showed that $$\Phi(G)$$ is nilpotent and, in so doing, developed a method of proof known today as Frattini's argument.

Besides group theory, he also studied differential geometry and the analysis of second degree indeterminates.