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Michio Suzuki (mathematician)
was a Japanese mathematician who studied group theory. Biography He was a professor at the University of Illinois at Urbana–Champaign from 1953 to his death. He also had visiting positions at the University of Chicago (1960–61), the Institute for Advanced Study (1962–63, 1968–69, spring 1981), the University of Tokyo (spring 1971), and the University of Padua (1994). Suzuki received his Ph.D. in 1952 from the University of Tokyo, despite having moved to the United States the previous year. He was the first to attack the Burnside conjecture, that every finite non-abelian simple group has even order. A notable achievement was his discovery in 1960 of the Suzuki groups, an infinite family of the only non-abelian simple groups whose order is not divisible by 3. The smallest, of order 29120, was the first simple group of order less than 1 million to be discovered since Dickson's list of 1900. He classified several classes of simple groups of small rank, including the CI ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Chiba, Chiba
is the capital city of Chiba Prefecture, Japan. It sits about east of the centre of Tokyo on Tokyo Bay. The city became a government-designated city in 1992. In June 2019, its population was 979,768, with a population density of 3,605 people per km2. The city has an area of . Chiba City is one of the Kantō region's primary seaports, and is home to Chiba Port, which handles one of the highest volumes of cargo in Japan. Much of the city is residential, although there are many factories and warehouses along the coast. There are several major urban centres in the city, including Makuhari, a prime waterfront business district in which Makuhari Messe is located, and Central Chiba, in which the prefectural government office and the city hall are located. Chiba is famous for the Chiba Urban Monorail, the longest suspended monorail in the world. Some popular destinations in the city include: Kasori Shell Midden, the largest shellmound in the world at , Inage Beach, the first artifici ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
CIT-group
The C-Group culture is an archaeological culture found in Lower Nubia, which dates from ca. 2400 BCE to ca. 1550 BCE. It was named by George A. Reisner. With no central site and no written evidence about what these people called themselves, Reisner assigned the culture a letter. The C-Group arose after Reisner's A-Group and B-Group cultures, and around the time the Old Kingdom was ending in Ancient Egypt. Overview While today many scholars see A and B as actually being a continuation of the same group, C-Group is considered as the product of Saharan pastoralist distinct. The C-Group is marked by its distinctive pottery, and for its tombs. Early C-Group tombs consisted of a simple "stone circle" with the body buried in a depression in the centre. The tombs later became more elaborate with the bodies being placed in a stone lined chamber, and then the addition of an extra chamber on the east: for offerings. The origins of the C-Group are still debated. Some scholars see it largel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Springer-Verlag
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in the 1990s and a sale to venture capitalists it fused with Wolters Kluwer and eventually became part of Springer Nature in 2015. Springer has major offices in Berlin, Heidelberg, Dordrecht, and New York City. History Julius Springer founded Springer-Verlag in Berlin in 1842 and his son Ferdinand Springer grew it from a small firm of 4 employees into Germany's then second largest academic publisher with 65 staff in 1872.Chronology ". Springer Science+Business Media. In 1964, Springer expanded its business internationally, o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brauer–Suzuki–Wall Theorem
In mathematics, the Brauer–Suzuki–Wall theorem, proved by , characterizes the one-dimensional unimodular projective groups over finite field In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any field, a finite field is a set on which the operations of multiplication, addition, subtr ...s. References * Theorems about finite groups {{Abstract-algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Brauer–Suzuki Theorem
In mathematics, the Brauer–Suzuki theorem, proved by , , , states that if a finite group has a generalized quaternion Sylow 2-subgroup and no non-trivial normal subgroups of odd order, then the group has a center of order 2. In particular, such a group cannot be simple. A generalization of the Brauer–Suzuki theorem is given by Glauberman's Z* theorem In mathematics, George Glauberman's Z* theorem is stated as follows: Z* theorem: Let ''G'' be a finite group, with ''O''(''G'') being its maximal normal subgroup of odd order. If ''T'' is a Sylow 2-subgroup of ''G'' containing an involution no .... References * * * gives a detailed proof of the Brauer–Suzuki theorem. * Theorems about finite groups {{Abstract-algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bender–Suzuki Theorem
In finite group theory, an area of abstract algebra, a strongly embedded subgroup of a finite group ''G'' is a proper subgroup ''H'' of even order such that ''H'' ∩ ''H''''g'' has odd order whenever ''g'' is not in ''H''. The Bender–Suzuki theorem, proved by extending work of , classifies the groups ''G'' with a strongly embedded subgroup ''H''. It states that either # ''G'' has cyclic or generalized quaternion Sylow 2-subgroups and ''H'' contains the centralizer of an involution # or ''G''/''O''(''G'') has a normal subgroup of odd index isomorphic to one of the simple groups PSL2(''q''), Sz(''q'') or PSU3(''q'') where ''q''≥4 is a power of 2 and ''H'' is ''O''(''G'')N''G''(''S'') for some Sylow 2-subgroup ''S''. revised Suzuki's part of the proof. extended Bender's classification to groups with a proper 2-generated core. References * * * * *{{Citation , last1=Suzuki , first1=Michio , author1-link=Michio Suzuki (mathematician) , title=On a class of doubly ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Baer–Suzuki Theorem
In mathematical finite group theory, the Baer–Suzuki theorem, proved by and , states that if any two elements of a conjugacy class In mathematics, especially group theory, two elements a and b of a group are conjugate if there is an element g in the group such that b = gag^. This is an equivalence relation whose equivalence classes are called conjugacy classes. In other wor ... ''C'' of a finite group generate a nilpotent subgroup, then all elements of the conjugacy class ''C'' are contained in a nilpotent subgroup. gave a short elementary proof. References * * * * Theorems about finite groups {{abstract-algebra-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Japanese Language
is spoken natively by about 128 million people, primarily by Japanese people and primarily in Japan, the only country where it is the national language. Japanese belongs to the Japonic or Japanese- Ryukyuan language family. There have been many attempts to group the Japonic languages with other families such as the Ainu, Austroasiatic, Koreanic, and the now-discredited Altaic, but none of these proposals has gained widespread acceptance. Little is known of the language's prehistory, or when it first appeared in Japan. Chinese documents from the 3rd century AD recorded a few Japanese words, but substantial Old Japanese texts did not appear until the 8th century. From the Heian period (794–1185), there was a massive influx of Sino-Japanese vocabulary into the language, affecting the phonology of Early Middle Japanese. Late Middle Japanese (1185–1600) saw extensive grammatical changes and the first appearance of European loanwords. The basis of the standard dialect moved f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ovoid (projective Geometry)
In projective geometry an ovoid is a sphere like pointset (surface) in a projective space of dimension . Simple examples in a real projective space are hyperspheres (quadrics). The essential geometric properties of an ovoid \mathcal O are: # Any line intersects \mathcal O in at most 2 points, # The tangents at a point cover a hyperplane (and nothing more), and # \mathcal O contains no lines. Property 2) excludes degenerated cases (cones,...). Property 3) excludes ruled surfaces (hyperboloids of one sheet, ...). An ovoid is the spatial analog of an oval in a projective plane. An ovoid is a special type of a ''quadratic set.'' Ovoids play an essential role in constructing examples of Möbius planes and higher dimensional Möbius geometries. Definition of an ovoid * In a projective space of dimension a set \mathcal O of points is called an ovoid, if : (1) Any line meets \mathcal O in at most 2 points. In the case of , g\cap\mathcal O, =0, the line is called a ''passing'' (o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jacques Tits
Jacques Tits () (12 August 1930 – 5 December 2021) was a Belgian-born French mathematician who worked on group theory and incidence geometry. He introduced Tits buildings, the Tits alternative, the Tits group, and the Tits metric. Life and career Tits was born in Uccle to Léon Tits, a professor, and Lousia André. Jacques attended the Athénée of Uccle and the Free University of Brussels. His thesis advisor was Paul Libois, and Tits graduated with his doctorate in 1950 with the dissertation ''Généralisation des groupes projectifs basés sur la notion de transitivité''. His academic career includes professorships at the Free University of Brussels (now split into the Université Libre de Bruxelles and the Vrije Universiteit Brussel) (1962–1964), the University of Bonn (1964–1974) and the Collège de France in Paris, until becoming emeritus in 2000. He changed his citizenship to French in 1974 in order to teach at the Collège de France, which at that point required ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Suzuki Sporadic Group
In the area of modern algebra known as group theory, the Suzuki group ''Suz'' or ''Sz'' is a sporadic simple group of order : 213 · 37 · 52 · 7 · 11 · 13 = 448345497600 : ≈ 4. History ''Suz'' is one of the 26 Sporadic groups and was discovered by as a rank 3 permutation group on 1782 points with point stabilizer G2(4). It is not related to the Suzuki groups of Lie type. The Schur multiplier has order 6 and the outer automorphism group has order 2. Complex Leech lattice The 24-dimensional Leech lattice has a fixed-point-free automorphism of order 3. Identifying this with a complex cube root of 1 makes the Leech lattice into a 12 dimensional lattice over the Eisenstein integers, called the complex Leech lattice. The automorphism group of the complex Leech lattice is the universal cover 6 · Suz of the Suzuki group. This makes the group 6 · Suz · 2 into a maximal subgroup of Conway's group Co0 = 2 · Co1 of automorphisms of the Leech lattice, and shows ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
