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Nottingham Group
In the mathematical field of infinite group theory, the Nottingham group is the group ''J''(F''p'') or ''N''(F''p'') consisting of formal power series ''t'' + ''a''2''t''2+... with coefficients in F''p''. The group multiplication is given by formal composition also called substitution. That is, if : f = t+ \sum_^\infty a_n t^n and if g is another element, then :gf = f(g) = g+ \sum_^\infty a_n g^n. The group multiplication is not abelian Abelian may refer to: Mathematics Group theory * Abelian group, a group in which the binary operation is commutative ** Category of abelian groups (Ab), has abelian groups as objects and group homomorphisms as morphisms * Metabelian group, a grou .... The group was studied by number theorists as the group of wild automorphisms of the local field F''p''((t)) and by group theorists including D. and the name "Nottingham group" refers to his former domicile. This group is a finitely generated pro-''p''-group, of finite width. For every finite g ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline. Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature orin modern mathematicsentities that are stipulated to have certain properties, called axioms. A ''proof'' consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, andin case of abstraction from naturesome basic properties that are considered true starting poin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Formal Power Series
In mathematics, a formal series is an infinite sum that is considered independently from any notion of convergence, and can be manipulated with the usual algebraic operations on series (addition, subtraction, multiplication, division, partial sums, etc.). A formal power series is a special kind of formal series, whose terms are of the form a x^n where x^n is the nth power of a variable x (n is a non-negative integer), and a is called the coefficient. Hence, power series can be viewed as a generalization of polynomials, where the number of terms is allowed to be infinite, with no requirements of convergence. Thus, the series may no longer represent a function of its variable, merely a formal sequence of coefficients, in contrast to a power series, which defines a function by taking numerical values for the variable within a radius of convergence. In a formal power series, the x^n are used only as position-holders for the coefficients, so that the coefficient of x^5 is the fift ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abelian Group
In mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on the order in which they are written. That is, the group operation is commutative. With addition as an operation, the integers and the real numbers form abelian groups, and the concept of an abelian group may be viewed as a generalization of these examples. Abelian groups are named after early 19th century mathematician Niels Henrik Abel. The concept of an abelian group underlies many fundamental algebraic structures, such as fields, rings, vector spaces, and algebras. The theory of abelian groups is generally simpler than that of their non-abelian counterparts, and finite abelian groups are very well understood and fully classified. Definition An abelian group is a set A, together with an operation \cdot that combines any two elements a and b of A to form another element of A, denoted a \cdot b. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pro-p Group
In mathematics, a pro-''p'' group (for some prime number ''p'') is a profinite group G such that for any open normal subgroup N\triangleleft G the quotient group G/N is a ''p''-group. Note that, as profinite groups are compact, the open subgroups are exactly the closed subgroups of finite index, so that the discrete quotient group is always finite. Alternatively, one can define a pro-''p'' group to be the inverse limit of an inverse system of discrete finite ''p''-groups. The best-understood (and historically most important) class of pro-''p'' groups is the ''p''-adic analytic groups: groups with the structure of an analytic manifold over \mathbb_p such that group multiplication and inversion are both analytic functions. The work of Lubotzky and Mann, combined with Michel Lazard's solution to Hilbert's fifth problem over the ''p''-adic numbers, shows that a pro-''p'' group is ''p''-adic analytic if and only if it has finite rank, i.e. there exists a positive integer r su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fesenko
Fesenko ( uk, Фесенко) is a Ukrainian surname. Notable people with this name include: *Ivan Fesenko (born 1962), Russian mathematician * Kyrylo Fesenko (born 1986), Ukrainian basketball player *Sergey Fesenko, Sr. (born 1959), Soviet swimmer *Serhiy Fesenko Sergey Fesenko Jr. (also spelled as Sergiy or Serhiy, born June 5, 1982) is a long-distance freestyle swimmer from Ukraine. He competed in the 2000 Olympic Games in Sydney, Australia, 2004 Olympic Games in Athens, Greece and qualified to r ... (born 1982), Ukrainian swimmer * Yekaterina Fesenko (born 1958), Soviet hurdler See also * {{surname, Fesenko Ukrainian-language surnames ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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 (mathematics), fields, and vector spaces, can all be seen as groups endowed with additional operation (mathematics), operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. Various physical systems, such as crystals and the hydrogen atom, and Standard Model, three of the four known fundamental forces in the universe, may be modelled by symmetry groups. Thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. Group theory is also ce ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Nottingham
This article is about the history of Nottingham. Pre-history The middle Trent Valley was covered by ice sheets for large parts of the Paleolithic period between 500,000 and 10,000 years ago, and evidence of early human activity is limited to a small number of discarded stone artefacts found in glacial outwash or boulder clays. The post-glacial warming of the climate in the Mesolithic period between 10,000BC and 4,000BC saw the Trent Valley colonised by hunter-gatherers taking advantage of the emerging mixed woodland environment. Flintwork dating from the period has been excavated on the site of Nottingham Castle, and stone tools used by hunter-gatherers have been found in areas of the city including Beeston, Wollaton Park and the site of the Victoria Centre. The Neolithic period between 4,000BC and 2,000BC saw the clearance of woodland and the transition of the area towards a settled agricultural society. Pottery from the period has been found in Attenborough and Holme Pierr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
