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arithmetic group

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  • Arithmetic group — In mathematics, an arithmetic group (arithmetic subgroup) in a linear algebraic group G defined over a number field K is a subgroup Γ of G ( K ) that is commensurable with G ( O ), where O is the ring of integers of K . Here two subgroups A and B …   Wikipedia

  • Arithmetic hyperbolic 3-manifold — In mathematics, an arithmetic hyperbolic 3 manifold is a hyperbolic 3 manifold whose fundamental group is an arithmetic group as a subgroup of PGL(2,C) …   Wikipedia

  • Arithmetic coding — is a method for lossless data compression. Normally, a string of characters such as the words hello there is represented using a fixed number of bits per character, as in the ASCII code. Like Huffman coding, arithmetic coding is a form of… …   Wikipedia

  • Arithmetic combinatorics — arose out of the interplay between number theory, combinatorics, ergodic theory and harmonic analysis. It is about combinatorial estimates associated with arithmetic operations (addition, subtraction, multiplication, and division). Additive… …   Wikipedia

  • Group theory — is a mathematical discipline, the part of abstract algebra that studies the algebraic structures known as groups. The development of group theory sprang from three main sources: number theory, theory of algebraic equations, and geometry. The… …   Wikipedia

  • Arithmetic function — In number theory, an arithmetic (or arithmetical) function is a real or complex valued function ƒ(n) defined on the set of natural numbers (i.e. positive integers) that expresses some arithmetical property of n. [1] An example of an arithmetic… …   Wikipedia

  • Group (mathematics) — This article covers basic notions. For advanced topics, see Group theory. The possible manipulations of this Rubik s Cube form a group. In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines …   Wikipedia

  • Arithmetic of abelian varieties — In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or family of those. It goes back to the studies of Fermat on what are now recognised as elliptic curves; and has become a very… …   Wikipedia

  • Group size measures — A group acts as a social environment of individuals: Great Woodswallows. Many animals, including humans, tend to live in groups, herds, flocks, bands, packs, shoals, or colonies (hereafter: groups) of conspecific individuals. The size of these… …   Wikipedia

  • arithmetic — Synonyms and related words: Boolean algebra, Euclidean geometry, Fourier analysis, Lagrangian function, algebra, algebraic geometry, analysis, analytic geometry, associative algebra, binary arithmetic, calculation, calculus, ciphering, circle… …   Moby Thesaurus

  • Group isomorphism — In abstract algebra, a group isomorphism is a function between two groups that sets up a one to one correspondence between the elements of the groups in a way that respects the given group operations. If there exists an isomorphism between two… …   Wikipedia

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