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László Pyber
''László Pyber'' (born 8 May 1960 in Budapest) is a Hungarian mathematician. He is a researcher at the Alfréd Rényi Institute of Mathematics, Budapest. He works in combinatorics and group theory. Biography Pyber received his Ph.D. from the Hungarian Academy of Sciences in 1989 under the direction of László Lovász and Gyula O.H. Katona with the thesis ''Extremal Structures and Covering Problems.'' In 2007, he was awarded the Academics Prize by the Hungarian Academy of Sciences. In 2017, he was the recipient of an ERC Advanced Grant. Mathematical contributions Pyber has solved a number of conjectures in graph theory. In 1985, he proved the conjecture of Paul Erdős and Tibor Gallai that edges of a simple graph with ''n'' vertices can be covered with at most ''n-1'' circuits and edges. In 1986, he proved the conjecture of Paul Erdős that a graph with ''n'' vertices and its complement can be covered with ''n''2/4+2 cliques. He has also contributed to the study ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Budapest
Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population of 1,752,286 over a land area of about . Budapest, which is both a city and county, forms the centre of the Budapest metropolitan area, which has an area of and a population of 3,303,786; it is a primate city, constituting 33% of the population of Hungary. The history of Budapest began when an early Celtic settlement transformed into the Roman town of Aquincum, the capital of Lower Pannonia. The Hungarians arrived in the territory in the late 9th century, but the area was pillaged by the Mongols in 1241–42. Re-established Buda became one of the centres of Renaissance humanist culture by the 15th century. The Battle of Mohács, in 1526, was followed by nearly 150 years of Ottoman rule. After the reconquest of Buda in 1686, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Classification Of Finite Simple Groups
In mathematics, the classification of the finite simple groups is a result of group theory stating that every finite simple group is either cyclic, or alternating, or it belongs to a broad infinite class called the groups of Lie type, or else it is one of twenty-six or twenty-seven exceptions, called sporadic. The proof consists of tens of thousands of pages in several hundred journal articles written by about 100 authors, published mostly between 1955 and 2004. Simple groups can be seen as the basic building blocks of all finite groups, reminiscent of the way the prime numbers are the basic building blocks of the natural numbers. The Jordan–Hölder theorem is a more precise way of stating this fact about finite groups. However, a significant difference from integer factorization is that such "building blocks" do not necessarily determine a unique group, since there might be many non-isomorphic groups with the same composition series or, put in another way, the extens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
21st-century Hungarian Mathematicians
The 1st century was the century spanning AD 1 (Roman numerals, I) through AD 100 (Roman numerals, C) according to the Julian calendar. It is often written as the or to distinguish it from the 1st century BC (or BCE) which preceded it. The 1st century is considered part of the Classical era, epoch, or History by period, historical period. The 1st century also saw the Christianity in the 1st century, appearance of Christianity. During this period, Europe, North Africa and the Near East fell under increasing domination by the Roman Empire, which continued expanding, most notably conquering Britain under the emperor Claudius (AD 43). The reforms introduced by Augustus during his long reign stabilized the empire after the turmoil of the previous century's civil wars. Later in the century the Julio-Claudian dynasty, which had been founded by Augustus, came to an end with the suicide of Nero in AD 68. There followed the famous Year of Four Emperors, a brief period of civil war and inst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Group Theorists
A group is a number of persons or things that are located, gathered, or classed together. Groups of people * Cultural group, a group whose members share the same cultural identity * Ethnic group, a group whose members share the same ethnic identity * Religious group (other), a group whose members share the same religious identity * Social group, a group whose members share the same social identity * Tribal group, a group whose members share the same tribal identity * Organization, an entity that has a collective goal and is linked to an external environment * Peer group, an entity of three or more people with similar age, ability, experience, and interest Social science * In-group and out-group * Primary, secondary, and reference groups * Social group * Collectives Science and technology Mathematics * Group (mathematics), a set together with a binary operation satisfying certain algebraic conditions Chemistry * Functional group, a group of atoms which provi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
László Babai
László "Laci" Babai (born July 20, 1950, in Budapest) a fellow of the American Academy of Arts and Sciences, and won the Knuth Prize. Babai was an invited speaker at the International Congresses of Mathematicians in Kyoto (1990), Zürich (1994, plenary talk), and Rio de Janeiro (2018). Sources Professor László Babai's algorithm is next big step in conquering isomorphism in graphs// Published on Nov 20, 2015 Division of the Physical Sciences / The University of Chicago Mathematician claims breakthrough in complexity theory by Adrian Cho 10 November 2015 17:45 // Posted iMath Science AAAS AAAS may refer to: * American Academy of Arts and Sciences, a learned society and center for policy research; the publisher of the journal ''Dædalus'' * American Association for the Advancement of Science, an organization that supports scientifi ... News A Quasipolynomial Time Algorithm for Graph Isomorphism: The Details+ Background on Graph Isomorphism + The Main Result // Math ∩ Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cayley Graph
In mathematics, a Cayley graph, also known as a Cayley color graph, Cayley diagram, group diagram, or color group is a graph that encodes the abstract structure of a group. Its definition is suggested by Cayley's theorem (named after Arthur Cayley), and uses a specified set of generators for the group. It is a central tool in combinatorial and geometric group theory. The structure and symmetry of Cayley graphs makes them particularly good candidates for constructing families of expander graphs. Definition Let G be a group and S be a generating set of G. The Cayley graph \Gamma = \Gamma(G,S) is an edge-colored directed graph constructed as follows: In his Collected Mathematical Papers 10: 403–405. * Each element g of G is assigned a vertex: the vertex set of \Gamma is identified with G. * Each element s of S is assigned a color c_s. * For every g \in G and s \in S, there is a directed edge of color c_s from the vertex corresponding to g to the one corresponding to gs. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
List Of Finite Simple Groups
A ''list'' is any set of items in a row. List or lists may also refer to: People * List (surname) Organizations * List College, an undergraduate division of the Jewish Theological Seminary of America * SC Germania List, German rugby union club Other uses * Angle of list, the leaning to either port or starboard of a ship * List (information), an ordered collection of pieces of information ** List (abstract data type), a method to organize data in computer science * List on Sylt, previously called List, the northernmost village in Germany, on the island of Sylt * ''List'', an alternative term for ''roll'' in flight dynamics * To ''list'' a building, etc., in the UK it means to designate it a listed building that may not be altered without permission * Lists (jousting), the barriers used to designate the tournament area where medieval knights jousted * ''The Book of Lists'', an American series of books with unusual lists See also * The List (other) * Listing ( ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Profinite Group
In mathematics, a profinite group is a topological group that is in a certain sense assembled from a system of finite groups. The idea of using a profinite group is to provide a "uniform", or "synoptic", view of an entire system of finite groups. Properties of the profinite group are generally speaking uniform properties of the system. For example, the profinite group is finitely generated (as a topological group) if and only if there exists d\in\N such that every group in the system can be generated by d elements. Many theorems about finite groups can be readily generalised to profinite groups; examples are Lagrange's theorem and the Sylow theorems. To construct a profinite group one needs a system of finite groups and group homomorphisms between them. Without loss of generality, these homomorphisms can be assumed to be surjective, in which case the finite groups will appear as quotient groups of the resulting profinite group; in a sense, these quotients approximate the pro ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Subgroup Growth
In mathematics, subgroup growth is a branch of group theory, dealing with quantitative questions about subgroups of a given group. Let G be a finitely generated group. Then, for each integer n define a_n(G) to be the number of subgroups H of index n in G. Similarly, if G is a topological group, s_n(G) denotes the number of open subgroups U of index n in G. One similarly defines m_n(G) and s_n^\triangleleft(G) to denote the number of maximal and normal subgroups of index n, respectively. Subgroup growth studies these functions, their interplay, and the characterization of group theoretical properties in terms of these functions. The theory was motivated by the desire to enumerate finite groups of given order, and the analogy with Mikhail Gromov's notion of word growth. Nilpotent groups Let G be a finitely generated torsionfree nilpotent group. Then there exists a composition series with infinite cyclic factors, which induces a bijection (though not necessarily a homo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Group
Finite is the opposite of infinite. It may refer to: * Finite number (other) * 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 for person and/or tense or aspect * "Finite", a song by Sara Groves from the album ''Invisible Empires ''Invisible Empires'' is the seventh studio album and tenth album overall from Christian singer and songwriter Sara Groves, and it released on October 18, 2011 by Fair Trade and Columbia Records. The producers on the album were Steve Hindalong an ...'' See also * * Nonfinite (other) {{disambiguation fr:Fini it:Finito ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
