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Frattini Property
Frattini is an Italian surname. Notable people with the surname include: * Angelo Frattini, sculptor * Franco Frattini, politician * Giovanni Frattini, mathematician ** Frattini argument ** 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 ... * Francesco Frattini, cyclist {{surname, Frattini Italian-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angelo Frattini
Angelo Frattini (10 November 1910 – 2 September 1975) was an Italian sculptor from Varese. He studied at Brera Academy and his first contacts with sculptural art were influenced by Scapigliatura's teachings. He also exhibited his works in New York City and Washington DC, where he was received by president Lyndon Johnson. Angelo Frattini died in Varese on September 2, 1975. In 1978 the artistic lyceum of his hometown was named after him. Life Born in Varese on November 10, 1910, Angelo Frattini became an orphan at the age of 9. His artistic formation took place initially in Naples and subsequently in Milan. Frattini served his Italian military service in Naples, where he attended Giovanni De Martino's evening classes and got to know Gemito's sculpture. In Naples he also frequented the Galleria d’Arte Moderna and the National Archeological Museum. For most of his youth he was self-taught, and was influenced by late Nineteenth Century art. In 1925 he was a student at G ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Franco Frattini
Franco Frattini (14 March 1957 – 24 December 2022) was an Italian politician and magistrate. From January to December 2022, Frattini served as president of the Council of State. Frattini previously served as Minister of Foreign Affairs from 2002 to 2004 and from 2008 to 2011 in the governments of Silvio Berlusconi and Minister of Public Function from 1995 to 1996 and from 2001 to 2002, in the government of Lamberto Dini and Silvio Berlusconi. From 2004 to 2008, he was also the European Commissioner for Justice, Freedom and Security in the first Barroso Commission. Education and career Frattini was born in Rome in 1957. He attended the "Giulio Cesare" Classical High School in Rome and graduated in law in 1979 at the Sapienza University. From 1984 he was State Attorney and magistrate of the Regional Administrative Court (TAR) in Piedmont. In 1986, Frattini was named member of the Italian Council of State and legal adviser of the Treasury Ministry. During these years, he se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 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 indete ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Frattini 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. The argument was taken by Frattini, as he himself admits, from a paper of Alfredo Capelli dated 1884.M. Brescia, F. de Giovanni, M. Trombetti"The True Story Behind Frattini’s Argument" ''Advances in Group Theory and Applications'' 3doi:10.4399/97888255036928/ref> Frattini's Argument Statement If G is a finite group with normal subgroup H, and if P is a Sylow ''p''-subgroup of H, then :G = N_(P)H where N_(P) denotes the normalizer of P in G and N_(P)H means the product of group subsets. Proof The group P is a Sylow p-subgroup of H, so every Sylow p-subgroup of H is an H-conjugate of P, that is, it is of the form h^Ph, for some h \in H (see Sylow theorems). Let g be any element of G. Since H is normal in G, the subgroup g^Pg is c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 defined by \Phi(G)=G. It is analogous to the Jacobson radical in the theory of rings, and intuitively can be thought of as the subgroup of "small elements" (see the "non-generator" characterization below). It is named after Giovanni Frattini, who defined the concept in a paper published in 1885. Some facts * \Phi(G) is equal to the set of all non-generators or non-generating elements of . A non-generating element of is an element that can always be removed from a generating set; that is, an element ''a'' of such that whenever is a generating set of containing ''a'', X \setminus \ is also a generating set of . * \Phi(G) is always a characteristic subgroup of ; in particular, it is always a normal subgroup of . * If is finite, then \Phi(G) is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Francesco Frattini
Francesco Frattini (born 18 January 1967, in Varese) is an Italian former road bicycle racer. Major results ;1995 :1st, Rund um den Henninger-Turm :1st, Stage 6, Bicicleta Vasca :1st, Setmana Catalana de Ciclisme ::1st, Stage 3 ;1996 :1st, Stage 4, Tour of the Basque Country The Tour of the Basque Country (Officially: ''Itzulia Basque Country'', es, Vuelta al País Vasco, links=no, eu, Euskal Herriko Itzulia) is an annual road cycling stage race held in the Spanish Basque Country in April. It is one of the races ... External links *Palmarès by cyclingbase.com 1967 births Italian male cyclists Living people Cyclists from Varese {{Italy-cycling-bio-1960s-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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