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Longer titles found: Free abelian group (view), Elementary abelian group (view), Non-abelian group (view), Finitely generated abelian group (view), Category of abelian groups (view), Rank of an abelian group (view), Torsion-free abelian group (view), Topological abelian group (view), Locally compact abelian group (view), Height (abelian group) (view), Metabelian group (view), Torsion abelian group (view), Norm (abelian group) (view), Gaussian distribution on a locally compact Abelian group (view)

searching for Abelian group 82 found (892 total)

alternate case: abelian group

Dold–Kan correspondence (808 words) [view diff] exact match in snippet view article find links to article

{\displaystyle n} th homotopy group of the corresponding simplicial abelian group, and a chain homotopy corresponds to a simplicial homotopy. (In fact

The abelian group of divisor classes up to algebraic equivalence is now called the Néron-Severi group; it is known to be a finitely-generated abelian group

In arithmetic geometry, the Mordell–Weil group is an abelian group associated to any abelian variety A {\displaystyle A} defined over a number field K

the singular homology of topological spaces. By definition, given an abelian group A and a scheme X of finite type over a field k, the theory is given

a field K with a valuation v taking values in an arbitrary ordered abelian group: (K,v) is spherically complete if every collection of balls that is

isomorphism classes of all line bundles on some topological space X forms an abelian group called the Picard group of X. One can also define a symmetric power

is a rational class, in the sense that it lies in the image of the abelian group homomorphism H k ( V , Q ) → H {\displaystyle H_{k}(V,\mathbb {Q} )\to

to the underlying abelian monoid of an abelian group B , {\displaystyle B,} there exists a unique abelian group morphism G ( A ) → B . {\displaystyle G(A)\to

Γ ( U , F ) {\displaystyle \Gamma (U,{\mathcal {F}})} is a torsion abelian group. Similarly, for a prime number p, we say a sheaf F {\displaystyle {\mathcal

the rank of the quotient of the valuation groups; here the rank of an abelian group A {\displaystyle A} is defined as dim Q ⁡ ( A ⊗ Q ) {\displaystyle \dim

related by FV = VF = [p], where [p] is the pth power homomorphism of an abelian group scheme. If G is the discrete group with n elements over the finite field

{\displaystyle (\cdot ,\cdot ):F^{*}\times F^{*}\rightarrow G} , where G is an abelian group, written multiplicatively, such that ( ⋅ , ⋅ ) {\displaystyle (\cdot

in the category of Lie algebras. In particular, it is a simplicial abelian group, and thus is subject to the Dold–Kan correspondence. Differential graded

where G {\displaystyle G} is a locally compact abelian group, splits. Every locally precompact abelian group belongs to S ( T ) {\displaystyle {\mathcal

highlighted their work on stationary measures and closed orbits for non-abelian group actions on homogeneous spaces, solving a long-standing conjecture of

Freiman's Theorem in finite fields. Let A and B be finite subsets of an abelian group; then the sum set is defined to be A + B = { a + b : a ∈ A , b ∈ B }

have the double centralizer property) if every endomorphism of the abelian group M which commutes with all R-endomorphisms of M is given by multiplication

the automata. Suppose G {\displaystyle G} is an ordered abelian group, meaning an abelian group with a total ordering < {\displaystyle <} respecting the

Borel part of quantum groups and often (e.g. when finite or over an abelian group) possess an arithmetic root system, multiple Dynkin diagrams and a PBW-basis

2-manifolds are classified by their genus, that is half the rank of the Abelian group Γ/[Γ,Γ], where Γ = π1(M). Moreover, it also follows from the theory

varieties. Chow varieties are distinct from Chow groups, which are the abelian group of all algebraic cycles on a variety (not necessarily projective space)

quotient Pic(V)/Pic0(V) is an abelian group NS(V), called the Néron–Severi group of V. This is a finitely-generated abelian group by the Néron–Severi theorem

(-\{e\}+B)} for A , B {\displaystyle A,B} sets in a (not necessarily abelian) group. This transformation has the property that A 1 + B 1 ⊂ A + B , A 2 +

conjugate, hence must map identically in an abelian group, since conjugation is trivial in an abelian group) can be mapped to Z m {\displaystyle Z_{m}}

finite Abelian group into the set of complex numbers on the unit circle, bent functions from a finite Abelian group into a finite Abelian group, non-Abelian

{\displaystyle M.} Inverse image functor – functor between categories of Abelian-group-valued sheaves induced by a continuous map between topological spaces;

of the ring of regular functions O(X) on X is a finitely generated abelian group of rank r -1. Suppose the base field is perfect. Any affine curve X

A {\displaystyle A} and S {\displaystyle S} be finite subsets of an abelian group with S {\displaystyle S} nonempty, and let K {\displaystyle K} be a

Let X be an abelian group such that X ≅ X ⊕ X (for example the direct sum of an infinite number of copies of any nonzero abelian group), and let R be

been progressing rapidly, although still much is open: The case of an abelian group was solved in 2005, but otherwise this phenomenon seems to be very rare

\mathbb {Z} [t,t^{-1}]} -module to H 1 X {\displaystyle H_{1}X} ie: as an abelian group it is identical to H 1 X {\displaystyle H_{1}X} but the covering transformation

discrete series representation of M and a unitary representation of the abelian group A. If the limit of discrete series representation is in fact a discrete

as "A unimodality result in the enumeration of subgroups of a finite abelian group" (Proc. AMS 1987), which concerned applications of algebraic combinatorics

{\displaystyle B} , and C {\displaystyle C} are finite subsets of an abelian group, then | A | | B + C | ≤ | A + B | | A + C | . {\displaystyle |A||B+C|\leq

the chain complex corresponding to A; in particular, it is a graded abelian group. Next, to multiply two elements, writing S 1 {\displaystyle S^{1}} for

{\displaystyle n} -torus viewed as an abelian group, and R n {\displaystyle \mathbb {R} ^{n}} can also be viewed as an abelian group of dimension n {\displaystyle

{\mathbb {Z} }}} is a compact Hausdorff abelian group, and thus its Pontryagin dual must be a discrete abelian group. In fact, the Pontryagin dual of Z ^

argument. Eckmann–Hilton duality Eilenberg–MacLane spaces Given an abelian group π, the Eilenberg–MacLane spaces K ( π , n ) {\displaystyle K(\pi ,n)}

{\displaystyle \beth _{2}} . Example: the theory of the integers viewed as an abelian group. | ( α + 1 ) n / G | − | α n / G | {\displaystyle |(\alpha +1)^{n}/G|-|\alpha

dimension. The unitary dual of a locally compact abelian group is another locally compact abelian group, and the Plancherel measure is proportional to the

Projective symplectic group, PSp2n(q), PSpn(q) (not recommended), S2n(q), Abelian group (archaic). O2n+(q), PΩ2n+(q). "Hypoabelian group" is an archaic name

coefficient ni is the multiplicity of Vi. The set of all r-cycles is the free abelian group Z r X = ⨁ V ⊆ X Z ⋅ [ V ] , {\displaystyle Z_{r}X=\bigoplus _{V\subseteq

1090/S0002-9904-1964-11248-9. —— (1966). "Szegö functions on a locally compact Abelian group with ordered dual". Transactions of the American Mathematical Society

-modules to the category of right R {\displaystyle R} -modules. The abelian group Q / Z {\displaystyle \mathbb {Q} /\mathbb {Z} } is divisible and therefore

theory. A homology G-manifold (without boundary) of dimension n over an abelian group G of coefficients is a locally compact topological space X with finite

Cor ⁡ ( X , Y ) {\displaystyle \operatorname {Cor} (X,Y)} be the free abelian group generated by elementary correspondences from X to Y; elements of Cor

scheme X of finite type over a field k and integers i and j, we have an abelian group Hi(X,Z(j)), with the usual Chow group being the special case C H i (

Scotia Birch and Swinnerton-Dyer conjecture relates the rank of the abelian group of points over a number field of an elliptic curve E to the order of

characters, defined as the functor that takes any S-scheme T to the abelian group of group scheme homomorphisms from the base change G T {\displaystyle

Cartan subalgebra h , {\displaystyle {\mathfrak {h}},} and let the abelian group A = Z [ [ h ∗ ] ] {\displaystyle A=\mathbb {Z} [[{\mathfrak {h}}^{*}]]}

of Alb ⁡ ( V ) {\displaystyle \operatorname {Alb} (V)} , which is an abelian group since Alb ⁡ ( V ) {\displaystyle \operatorname {Alb} (V)} is an abelian

product of the corresponding Cayley graphs. Thus the Cayley graph of the abelian group Z 2 {\displaystyle \mathbb {Z} ^{2}} with the set of generators consisting

Right abelian group A right simple and conditionally commutative semigroup. The direct product of a right zero semigroup and an abelian group. Nagy p

very well known. Let D ( S ) {\displaystyle {\mathcal {D}}(S)} be the abelian group consisting of all the divisors on S. Then due to the intersection theorem

abelian variety. The quotient Pic(V)/Pic0(V) is a finitely-generated abelian group denoted NS(V), the Néron–Severi group of V. In other words, the Picard

copies of the genus 6 quintic X5 + Y5 + Z5 =0, and G to be an elementary abelian group of order 25, with suitable actions on the two curves. Hodge diamond:

given by ρ(a)v = av is a ring homomorphism. More generally, given an abelian group M, a module structure on M over a ring R is equivalent to giving a ring

in the group Z / 7 Z {\displaystyle \mathbb {Z} /7\mathbb {Z} } (an abelian group written additively) is the subset {1,2,4}. The development of this difference

infinitely generated examples of non-linear groups: for example the infinite abelian group (Z/2Z)N x (Z/3Z)N cannot be linear. Since the symmetric group on an

(x ⊕ x)2 = x2 ⊕ x2 ⊕ x2 ⊕ x2 = x ⊕ x ⊕ x ⊕ x and since (R, ⊕) is an abelian group, we can subtract x ⊕ x from both sides of this equation, which gives

{Fitt} _{i}(M)} are zero for i<n and R for i ≥ n. If M is a finite abelian group of order | M | {\displaystyle |M|} (considered as a module over the

rational equivalence form the Chow ring. Let Z*(X) := Z[X] be the free abelian group on the algebraic cycles of X. Then an adequate equivalence relation

=(-1)^{k}} . More precisely, L 2 k ( R ) {\displaystyle L_{2k}(R)} is the abelian group of equivalence classes [ ψ ] {\displaystyle [\psi ]} of non-degenerate

properties of codes. She worked on cyclic codes, generalizing them to Abelian group codes. With H.B. Mann, MacWilliams gave a solution to a difficult problem

irreducible representation is trivial on the center of K (a finite abelian group), 0 is a weight. To prove the characterization of Borel and de Siebenthal

an embedding of A × / U {\displaystyle A^{\times }/U} into the free Abelian group generated by the elements of P {\displaystyle P} . Thus, using the multiplicative

of a set M and an ultrapseudometric d on M. In the case when M is an Abelian group (written additively) and d is generated by a length function ‖ ⋅ ‖ {\displaystyle

Galois group Gal(L/F) is an extension of the group Gal(K/F) by the abelian group Gal(L/K), and this extension corresponds to an element of the cohomology

of a set M and an ultrapseudometric d on M. In the case when M is an Abelian group (written additively) and d is generated by a length function ‖ ⋅ ‖ {\displaystyle

Galois group Gal(L/F) is an extension of the group Gal(K/F) by the abelian group Gal(L/K), and this extension corresponds to an element of the cohomology

natural projection. Suppose that G {\displaystyle G} is a locally compact abelian group that contains the unit circle T {\displaystyle \mathbb {T} } as a subgroup

_{p})/\mathbb {Q} )\cong \mathbb {Z} /(p-1)\mathbb {Z} } In fact, any finite abelian group can be found as the Galois group of some subfield of a cyclotomic field

the singular cohomology group Hi(X,A) with coefficients in a given abelian group A, for fixed i > 0; then the representing space for F is the Eilenberg–MacLane

JSTOR 2238330. Kemperman, J. H. B. (1960). "On small sumsets in an abelian group". Acta Mathematica. 103 (1–2): 63–88. doi:10.1007/BF02546525. "Obituary:

received a Sloan Fellowship. Griffith, Phillip A. (1970), Infinite abelian group theory, The University of Chicago Press, Chicago, Ill.-London, ISBN 978-0-226-30870-8

is a semidirect product of an abelian group of order mn/p by the symmetric group Sym(n); the elements of the abelian group are of the form (θa1, θa2, .

that A(K), the group of points on A over K, is a finitely-generated abelian group. A great deal of information about its possible torsion subgroups is

{\underline {\mathbb {R} }}} be the constant sheaf on M associated to the abelian group R {\textstyle \mathbb {R} } ; in other words, R _ {\textstyle {\underline

the asterisk denotes the Pontryagin dual of a given locally compact abelian group. All of these statements were presented by Tate in a more general form

Hamilton's method, let us first recall the much simpler case of the Abelian group of translations in Euclidean three-dimensional space. Each translation

appropriate fixed space, up to homotopy equivalence. For example, for any abelian group G, and any based CW-complex X, the set [ X , K ( G , n ) ] {\displaystyle

simplicial group is always fibrantpg 12. In particular, for a simplicial abelian group, its geometric realization is homotopy equivalent to a product of Eilenberg-Maclane