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, structure, space, models, and change. History On ...

, 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 an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...

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 appoint ...

, Eugenio Beltrami, 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 alge ...

, 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 ceremony ...

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

subgroup In group theory, a branch of mathematics, given a group ''G'' under a binary operation ∗, a subset ''H'' of ''G'' is called a subgroup of ''G'' if ''H'' also forms a group under the operation ∗. More precisely, ''H'' is a subgroup ...

of a

finite group Finite is the opposite of infinite. It may refer to: * Finite number (disambiguation) * Finite set, a set whose cardinality (number of elements) is some natural number * Finite verb, a verb form that has a subject, usually being inflected or marked ...

. 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 de ...

, 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 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 was introduced by Benjamin Peirce in the context of his work on the class ...

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. T ...

. 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