Giovanni Frattini (8 January 1852 – 21 July 1925) was an Italian

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

, noted for his contributions to

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

Biography

Frattini entered the University of Rome in 1869, where he studied

mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

with

Giuseppe Battaglini __NOTOC__ Giuseppe Battaglini (11 January 1826 – 29 April 1894) was an Italian mathematician.D'Ovidio (1895). He studied mathematics at the Scuola d'Applicazione di Ponti e Strade (School of Bridges and Roads) of Naples. In 1860 he was appointe ...

Eugenio Beltrami Eugenio Beltrami (16 November 1835 – 18 February 1900) was an Italian mathematician notable for his work concerning differential geometry and mathematical physics. His work was noted especially for clarity of exposition. He was the first to ...

, and

Luigi Cremona Antonio Luigi Gaudenzio Giuseppe Cremona (7 December 1830 – 10 June 1903) was an Italian mathematician. His life was devoted to the study of geometry and reforming advanced mathematical teaching in Italy. He worked on algebraic curves and alg ...

, obtaining his

Laurea In Italy, the ''laurea'' is the main post-secondary academic degree. The name originally referred literally to the laurel wreath, since ancient times a sign of honor and now worn by Italian students right after their official graduation ceremo ...

in 1875. In 1885 he published a paper where he defined a certain

subgroup In group theory, a branch of mathematics, a subset of a group G is a subgroup of G if the members of that subset form a group with respect to the group operation in G. Formally, given a group (mathematics), group under a binary operation ...

of a

finite group In abstract algebra, a finite group is a group whose underlying set is finite. Finite groups often arise when considering symmetry of mathematical or physical objects, when those objects admit just a finite number of structure-preserving tra ...

. This subgroup, now known as the

Frattini subgroup In mathematics, particularly in group theory, the Frattini subgroup \Phi(G) of a group is the intersection of all maximal subgroups of . For the case that has no maximal subgroups, for example the trivial group or a Prüfer group, it is def ...

, is the subgroup

\Phi(G)

generated by all the non-generators of the group

G

. He showed that

\Phi(G)

nilpotent In mathematics, an element x of a ring (mathematics), ring R is called nilpotent if there exists some positive integer n, called the index (or sometimes the degree), such that x^n=0. The term, along with its sister Idempotent (ring theory), idem ...

and, in so doing, developed a method of proof known today as

Frattini's argument In group theory, a branch of mathematics, Frattini's argument is an important lemma in the structure theory of finite groups. It is named after Giovanni Frattini, who used it in a paper from 1885 when defining the Frattini subgroup of a group. ...

. Besides group theory, he also studied differential geometry and the analysis of second degree indeterminates. Emaldi, Maurizio, Giovanni Frattini 1852–1925, Irish Math. Soc. Bull. No. 23 (1989), 57–61.

Notes

References

* * Emaldi, M.; Zacher, G., ''Giovanni Frattini (1852–1925), matematico'' (in italian), Advances in group theory 2002, 191–207, Aracne, Rome, 2003.

External links

* * {{DEFAULTSORT:Frattini, Giovanni 1852 births 1925 deaths Scientists from Rome 19th-century Italian mathematicians 20th-century Italian mathematicians Group theorists Sapienza University of Rome alumni