doctoral_advisor death_date death_place birth_place image_size nationality field birth_date image article_title name
giuseppe battaglini eugenio beltrami 21 july 1925 rome , italy rome , italy 180px italian mathematics 8 january 1852 giovanni frattini.jpg giovanni frattini
 giovanni frattini
giovanni frattini

giovanni frattini -lrb- 8 january 1852 -- 21 july 1925 -rrb- was an italian mathematician , noted for his contributions to group theory .
he entered the university of rome in 1869 , where he studied mathematics with giuseppe battaglini , eugenio beltrami , and luigi cremona , obtaining his ph.d. 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 -lrb- `` g '' -rrb- generated by all the non-generators of the group `` g '' .
he showed that Φ -lrb- `` g '' -rrb- is nilpotent and , in so doing , developed a method of proof known today as frattini 's argument .
