In mathematics, an arithmetic group is a group obtained as the integer points of an algebraic group, for example They arise naturally in the study of arithmetic properties of quadratic forms and other classical topics in number theory. They also give rise to very interesting examples of Riemannian manifolds and hence are objects of interest in differential geometry and topology. Finally, these two topics join in the theory of automorphic forms which is fundamental in modern number theory.
In mathematics, an arithmeticgroup is a group obtained as the integer points of an algebraic group, for example S L 2 ( Z ) . {\displaystyle \mathrm {SL}...
Arithmetic is an elementary branch of mathematics that studies numerical operations like addition, subtraction, multiplication, and division. In a wider...
Arithmetic Fuchsian groups are a special class of Fuchsian groups constructed using orders in quaternion algebras. They are particular instances of arithmetic...
congruence subgroups in an arithmeticgroup provides it with a wealth of subgroups, in particular it shows that the group is residually finite. An important...
finite. crystallographic point group congruence subgroup arithmeticgroup geometric group theory computational group theory freely discontinuous free...
Margulis arithmeticity theorem says, in particular: for a simple Lie group G of real rank at least 2, every lattice in G is an arithmeticgroup. In seeking...
In mathematics and statistics, the arithmetic mean ( /ˌærɪθˈmɛtɪk ˈmiːn/ arr-ith-MET-ik), arithmetic average, or just the mean or average (when the context...
In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers...
work on modular arithmetic and additive and multiplicative groups related to quadratic fields. Early results about permutation groups were obtained by...
an abstract group, and to say that one has a group action of the abstract group that consists of performing the transformations of the group of transformations...
In mathematics, given two groups, (G,∗) and (H, ·), a group homomorphism from (G,∗) to (H, ·) is a function h : G → H such that for all u and v in G it...
In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus...
Grothendieck–Riemann–Roch theorem to arithmetic varieties. For this one defines arithmetic Chow groups CHp(X) of an arithmetic variety X, and defines Chern classes...
Quaternionic, Fermionic". Retrieved 1 February 2012. Milne, Algebraic Groups and ArithmeticGroups, p. 103 Bak, Anthony (1969), "On modules with quadratic forms"...
(this results from the fundamental theorem of arithmetic). The center Z ( G ) {\displaystyle Z(G)} of a group G {\displaystyle G} is the set of elements...
the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group operation is the...
In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused...
In mathematics, topological groups are the combination of groups and topological spaces, i.e. they are groups and topological spaces at the same time...
In mathematics, the orthogonal group in dimension n, denoted O(n), is the group of distance-preserving transformations of a Euclidean space of dimension...
Schneider and Heckenberger have generally proven the existence of an arithmetic root system also in the nonabelian case, generating a PBW basis as proven...
mathematics, the circle group, denoted by T {\displaystyle \mathbb {T} } or S 1 {\displaystyle \mathbb {S} ^{1}} , is the multiplicative group of all complex numbers...
In mathematics, a permutation group is a group G whose elements are permutations of a given set M and whose group operation is the composition of permutations...
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