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Dade Isometry
In mathematical finite group theory, the Dade isometry is an isometry from class function on a subgroup ''H'' with support on a subset ''K'' of ''H'' to class functions on a group ''G'' . It was introduced by as a generalization and simplification of an isometry used by in their proof of the odd order theorem, and was used by in his revision of the character theory of the odd order theorem. Definitions Suppose that ''H'' is a subgroup of a finite group ''G'', ''K'' is an invariant subset of ''H'' such that if two elements in ''K'' are conjugate in ''G'', then they are conjugate in ''H'', and π a set of primes containing all prime divisors of the orders of elements of ''K''. The Dade lifting is a linear map ''f'' → ''f''σ from class functions ''f'' of ''H'' with support on ''K'' to class functions ''f''σ of ''G'', which is defined as follows: ''f''σ(''x'') is ''f''(''k'') if there is an element ''k'' ∈ ''K'' conjugate to the π-part of ''x'', and 0 ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Group Theory
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'' See also * * Nonfinite (other) Nonfinite is the opposite of finite * a nonfinite verb is a verb that is not capable of serving as the main verb in an independent clause * a non-finite clause In linguistics, a non-finite clause is a dependent or embedded clause that represen ... {{disambiguation fr:Fini it:Finito ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isometry
In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective. The word isometry is derived from the Ancient Greek: ἴσος ''isos'' meaning "equal", and μέτρον ''metron'' meaning "measure". Introduction Given a metric space (loosely, a set and a scheme for assigning distances between elements of the set), an isometry is a transformation which maps elements to the same or another metric space such that the distance between the image elements in the new metric space is equal to the distance between the elements in the original metric space. In a two-dimensional or three-dimensional Euclidean space, two geometric figures are congruent if they are related by an isometry; the isometry that relates them is either a rigid motion (translation or rotation), or a composition of a rigid motion and a reflection. Isometries are often used in constructions where one space i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Class Function
In mathematics, especially in the fields of group theory and representation theory of groups, a class function is a function on a group ''G'' that is constant on the conjugacy classes of ''G''. In other words, it is invariant under the conjugation map on ''G''. Such functions play a basic role in representation theory. Characters The character of a linear representation of ''G'' over a field ''K'' is always a class function with values in ''K''. The class functions form the center of the group ring ''K'' 'G'' Here a class function ''f'' is identified with the element \sum_ f(g) g. Inner products The set of class functions of a group ''G'' with values in a field ''K'' form a ''K''-vector space. If ''G'' is finite and the characteristic of the field does not divide the order of ''G'', then there is an inner product defined on this space defined by \langle \phi , \psi \rangle = \frac \sum_ \phi(g) \psi(g^) where , ''G'', denotes the order of ''G''. The set of irred ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Support (mathematics)
In mathematics, the support of a real-valued function f is the subset of the function domain containing the elements which are not mapped to zero. If the domain of f is a topological space, then the support of f is instead defined as the smallest closed set containing all points not mapped to zero. This concept is used very widely in mathematical analysis. Formulation Suppose that f : X \to \R is a real-valued function whose domain is an arbitrary set X. The of f, written \operatorname(f), is the set of points in X where f is non-zero: \operatorname(f) = \. The support of f is the smallest subset of X with the property that f is zero on the subset's complement. If f(x) = 0 for all but a finite number of points x \in X, then f is said to have . If the set X has an additional structure (for example, a topology), then the support of f is defined in an analogous way as the smallest subset of X of an appropriate type such that f vanishes in an appropriate sense on its complement. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Odd Order Theorem
Odd means unpaired, occasional, strange or unusual, or a person who is viewed as eccentric. Odd may also refer to: Acronym * ODD (Text Encoding Initiative) ("One Document Does it all"), an abstracted literate-programming format for describing XML schemas * Oodnadatta Airport (IATA: ODD), South Australia * Oppositional defiant disorder, a mental disorder characterized by anger-guided, hostile behavior * Operational due diligence * Operational Design Domain (ODD) in case of autonomous cars * Optical disc drive * ''ODD'', a 2007 play by Hal Corley about a teenager with oppositional defiant disorder Mathematics * Even and odd numbers, an integer is odd if dividing by two does not yield an integer * Even and odd functions, a function is odd if ''f''(−''x'') = −''f''(''x'') for all ''x'' * Even and odd permutations, a permutation of a finite set is odd if it is composed of an odd number of transpositions Ships * HNoMS ''Odd'', a Storm-class patrol boat of the Royal No ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Feit–Thompson Proof
Feit–Thompson may refer to: * Feit–Thompson conjecture * Feit–Thompson theorem In mathematics, the Feit–Thompson theorem, or odd order theorem, states that every finite group of odd order is solvable. It was proved by . History conjectured that every nonabelian finite simple group has even order. suggested using th ... {{disambiguation ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cambridge University Press
Cambridge University Press is the university press of the University of Cambridge. Granted letters patent by Henry VIII of England, King Henry VIII in 1534, it is the oldest university press A university press is an academic publishing house specializing in monographs and scholarly journals. Most are nonprofit organizations and an integral component of a large research university. They publish work that has been reviewed by schola ... in the world. It is also the King's Printer. Cambridge University Press is a department of the University of Cambridge and is both an academic and educational publisher. It became part of Cambridge University Press & Assessment, following a merger with Cambridge Assessment in 2021. With a global sales presence, publishing hubs, and offices in more than 40 Country, countries, it publishes over 50,000 titles by authors from over 100 countries. Its publishing includes more than 380 academic journals, monographs, reference works, school and uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Annals Of Mathematics
The ''Annals of Mathematics'' is a mathematical journal published every two months by Princeton University and the Institute for Advanced Study. History The journal was established as ''The Analyst'' in 1874 and with Joel E. Hendricks as the founding editor-in-chief. It was "intended to afford a medium for the presentation and analysis of any and all questions of interest or importance in pure and applied Mathematics, embracing especially all new and interesting discoveries in theoretical and practical astronomy, mechanical philosophy, and engineering". It was published in Des Moines, Iowa, and was the earliest American mathematics journal to be published continuously for more than a year or two. This incarnation of the journal ceased publication after its tenth year, in 1883, giving as an explanation Hendricks' declining health, but Hendricks made arrangements to have it taken over by new management, and it was continued from March 1884 as the ''Annals of Mathematics''. The n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Finite Groups
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'' See also * * Nonfinite (other) Nonfinite is the opposite of finite * a nonfinite verb is a verb that is not capable of serving as the main verb in an independent clause * a non-finite clause In linguistics, a non-finite clause is a dependent or embedded clause that represen ... {{disambiguation fr:Fini it:Finito ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
