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searching for Quotient group 52 found (324 total)

Induced homomorphism (1,329 words) [view diff] no match in snippet view article find links to article

In mathematics, especially in algebraic topology, an induced homomorphism is a homomorphism derived in a canonical way from another map. For example, a

Hurwitz surface (648 words) [view diff] exact match in snippet view article find links to article

normal subgroup of the (ordinary) (2,3,7) triangle group. The finite quotient group is precisely the automorphism group. Automorphisms of complex algebraic

Fontaine–Mazur conjecture (322 words) [view diff] exact match in snippet view article find links to article

Tate twist of an even representation that factors through a finite quotient group of G a l ( Q ¯ | Q ) {\displaystyle \mathrm {Gal} ({\overline {\mathbb

Inflation-restriction exact sequence (414 words) [view diff] exact match in snippet view article find links to article

G, i.e., a homomorphism from G to the automorphism group of A. The quotient group G/N acts on AN = { a ∈ A : na = a for all n ∈ N}. Then the inflation-restriction

Torsion group (635 words) [view diff] exact match in snippet view article find links to article

additive group of the ring of polynomials over a finite field, and the quotient group of the rationals by the integers, as well as their direct summands,

Nilpotent space (520 words) [view diff] exact match in snippet view article find links to article

G_{n_{i}}^{i}=1} such that the induced action of π {\displaystyle \pi } on the quotient group G k i / G k + 1 i {\displaystyle G_{k}^{i}/G_{k+1}^{i}} is trivial for

Massey product (1,885 words) [view diff] exact match in snippet view article find links to article

exact, in which case all its elements are in the same element of the quotient group H ∗ ( Γ ) / ( [ u ] H ∗ ( Γ ) + H ∗ ( Γ ) [ w ] ) . {\displaystyle \displaystyle

Automorphic function (497 words) [view diff] exact match in snippet view article find links to article

automorphy for Γ {\displaystyle \Gamma } corresponds to a line bundle on the quotient group G / Γ {\displaystyle G/\Gamma } . Further, the automorphic forms for

2003–04 Duleep Trophy (137 words) [view diff] case mismatch in snippet view article find links to article

Team Matches Won Lost Drawn (WF) Drawn (LF) No result Points Quotient Group A North Zone 2 2 0 0 0 0 8 1.175 West Zone 2 0 1 0 0 1 1 0.983 Central Zone

2002–03 Ranji Trophy (382 words) [view diff] no match in snippet view article find links to article

Baroda qualified to the knockouts ahead of Punjab on a better run-quotient. Group A Kerala and Vidarbha qualified for the Plate Group knockout stage

Capable group (107 words) [view diff] exact match in snippet view article find links to article

Baer, Reinhold (1938), "Groups with preassigned central and central quotient group", Transactions of the American Mathematical Society, 44 (3): 387–412

Exact sequence (2,577 words) [view diff] exact match in snippet view article find links to article

second homomorphism maps each element i in Z to an element j in the quotient group; that is, j = i mod 2. Here the hook arrow ↪ {\displaystyle \hookrightarrow

Generalized Jacobian (557 words) [view diff] exact match in snippet view article find links to article

1-form over a 1-cycle. The analytic generalized Jacobian is then the quotient group Ω(−m)*/H1(C − S). Rosenlicht, Maxwell (1954), "Generalized Jacobian

Polycyclic group (539 words) [view diff] exact match in snippet view article find links to article

a normal subgroup of Gi+1 (for every i between 0 and n - 1) and the quotient group Gi+1 / Gi is a cyclic group (for every i between 0 and n - 1) A metacyclic

Local class field theory (1,047 words) [view diff] exact match in snippet view article find links to article

extension L of K the reciprocity map induces an isomorphism of the quotient group K×/N(L×) of K× by the norm group N(L×) of the extension L× to the Galois

Pure subgroup (692 words) [view diff] exact match in snippet view article find links to article

subgroup is pure. A divisible subgroup of an abelian group is pure. If the quotient group is torsion-free, the subgroup is pure. The torsion subgroup of an abelian

Robert Langlands (1,990 words) [view diff] exact match in snippet view article find links to article

identified with characters of local multiplicative groups and the idele quotient group, respectively; (b) earlier results of Martin Eichler and Goro Shimura

Snake lemma (1,524 words) [view diff] exact match in snippet view article find links to article

simple, the right vertical arrow has trivial cokernel. Meanwhile the quotient group S 3 / C 3 {\displaystyle S_{3}/C_{3}} is isomorphic to C 2 {\displaystyle

Torsion subgroup (924 words) [view diff] exact match in snippet view article find links to article

The 4-torsion subgroup of the quotient group of the complex numbers under addition by a lattice.

Exotic sphere (3,844 words) [view diff] exact match in snippet view article find links to article

Bernoulli numbers; this article uses the number theorists' convention.) The quotient group Θ n / b P n + 1 {\displaystyle \Theta _{n}/bP_{n+1}} has a description

Glossary of functional analysis (3,200 words) [view diff] exact match in snippet view article find links to article

theorem. index group The index group of a unital Banach algebra is the quotient group G ( A ) / G 0 ( A ) {\displaystyle G(A)/G_{0}(A)} where G ( A ) {\displaystyle

Basic subgroup (331 words) [view diff] exact match in snippet view article find links to article

order pn and infinite cyclic groups; B is a p-pure subgroup of A; The quotient group, A/B, is a p-divisible group. Conditions 1–3 imply that the subgroup

Transgression map (468 words) [view diff] exact match in snippet view article find links to article

G, i.e., a homomorphism from G to the automorphism group of A. The quotient group G / N {\displaystyle G/N} acts on A N = { a ∈ A : n a = a for all

Transgression map (468 words) [view diff] exact match in snippet view article find links to article

G, i.e., a homomorphism from G to the automorphism group of A. The quotient group G / N {\displaystyle G/N} acts on A N = { a ∈ A : n a = a for all

Construction of the real numbers (4,202 words) [view diff] exact match in snippet view article find links to article

subgroup, and the underlying additive group of the real number is the quotient group. To add real numbers defined this way we add the almost homomorphisms

Collineation (1,751 words) [view diff] exact match in snippet view article find links to article

preserving a projective semi-linear structure". Correspondingly, the quotient group PΓL / PGL ≅ Gal(K/k) corresponds to "choices of linear structure", with

Atkin–Lehner theory (712 words) [view diff] exact match in snippet view article find links to article

index 2s (where s is the number of distinct prime factors of N); the quotient group is isomorphic to (Z/2Z)s and acts on the cusp forms via the Atkin–Lehner

Minimal polynomial (field theory) (1,447 words) [view diff] exact match in snippet view article

{\displaystyle \alpha } . Hence the minimal polynomial can be found using the quotient group Gal ( Q ( 2 , 3 ) / Q ) / Gal ( Q ( 3 ) / Q ) {\displaystyle {\text{Gal}}(\mathbb

Cremona group (1,133 words) [view diff] exact match in snippet view article find links to article

( x 1 , . . . , x r ) {\displaystyle k(x_{1},...,x_{r})} , and the quotient group is the Cremona group of k ( x 1 , . . . , x r ) {\displaystyle k(x_{1}

Cayley's theorem (1,626 words) [view diff] exact match in snippet view article find links to article

defined to be the intersection of the conjugates of H in G. Then the quotient group G / N {\displaystyle G/N} is isomorphic to a subgroup of Sym ⁡ ( G /

School Psychological Examiner (1,256 words) [view diff] case mismatch in snippet view article find links to article

Assessment and Evaluation of the Individual Individual Intelligence quotient Group Assessment Diagnostics and Remedial Reading Ethical issues in education

Model theory (9,040 words) [view diff] exact match in snippet view article find links to article

original structure via an equivalence relation. An important example is a quotient group of a group. One might say that to understand the full structure one

Nonabelian Hodge correspondence (5,131 words) [view diff] exact match in snippet view article find links to article

This is because for an abelian group, every subgroup is normal, so the quotient group H ˇ k ( X , F ) = Z k ( X , F ) / B k ( X , F ) {\displaystyle {\check

K3 surface (5,241 words) [view diff] exact match in snippet view article find links to article

O(Pic(X)), and the automorphism group of X is commensurable with the quotient group O(Pic(X))/W. A related statement, due to Hans Sterk, is that Aut(X)

Spin structure (4,369 words) [view diff] exact match in snippet view article find links to article

central extension of SO(n) by S1. Viewed another way, SpinC(n) is the quotient group obtained from Spin(n) × Spin(2) with respect to the normal Z2 which

Lie algebra (10,462 words) [view diff] exact match in snippet view article find links to article

addition given by the group multiplication (which is abelian on each quotient group G i / G i + 1 {\displaystyle G_{i}/G_{i+1}} ), and with Lie bracket

Projective representation (4,249 words) [view diff] exact match in snippet view article find links to article

operator A ∈ G L ( V ) {\displaystyle A\in \mathrm {GL} (V)} in the quotient group P G L ( V ) {\displaystyle \mathrm {PGL} (V)} . Since T a {\displaystyle

Double coset (3,048 words) [view diff] exact match in snippet view article find links to article

normal, so that the H-double cosets are the same as the elements of the quotient group G / H, then the product on Z[H \ G / H] is the product in the group

Class formation (2,674 words) [view diff] exact match in snippet view article find links to article

F is a normal subgroup of E, and a cyclic layer if in addition the quotient group is cyclic. If E is a subgroup of G, then AE is defined to be the elements

Adjoint functors (9,995 words) [view diff] exact match in snippet view article find links to article

left adjoint called abelianization which assigns to every group G the quotient group Gab=G/[G,G]. The Grothendieck group. In K-theory, the point of departure

Co-Hopfian group (1,533 words) [view diff] exact match in snippet view article find links to article

additive group of rational numbers Q {\displaystyle \mathbb {Q} } and the quotient group Q / Z {\displaystyle \mathbb {Q} /\mathbb {Z} } are co-Hopfian. The

Divisor (algebraic geometry) (6,609 words) [view diff] exact match in snippet view article

irreducible of codimension one, then Cl(X − Z) is isomorphic to the quotient group of Cl(X) by the class of Z. If Z has codimension at least 2 in X, then

Arf invariant (3,422 words) [view diff] exact match in snippet view article find links to article

a field K of characteristic 2, Artin–Schreier theory identifies the quotient group of K by the subgroup U above with the Galois cohomology group H1(K,

Tensor product of modules (8,470 words) [view diff] exact match in snippet view article find links to article

subring of a ring R, then M ⊗ R N {\displaystyle M\otimes _{R}N} is the quotient group of M ⊗ S N {\displaystyle M\otimes _{S}N} by the subgroup generated

Symmetric product (topology) (3,282 words) [view diff] exact match in snippet view article

When establishing the Dold-Thom theorem, they also considered the "quotient group" Z[X] of SP(X). This is the free abelian group over X with the basepoint

Differential geometry of surfaces (17,444 words) [view diff] exact match in snippet view article find links to article

}}\end{pmatrix}}:\zeta \in \mathbf {C} ,\,|\zeta |=1\right\}.} The quotient group SU(1,1)/±I is the group of orientation-preserving isometries of D. Any

Cannon–Thurston map (4,116 words) [view diff] exact match in snippet view article find links to article

word-hyperbolic groups and H is normal in G then, by a result of Mosher, the quotient group Q = G/H is also word-hyperbolic. In this setting Mitra also described

Fundamental polygon (5,997 words) [view diff] exact match in snippet view article find links to article

segments and with the standard labelling. The abelianisation of Γ, the quotient group Γ/[Γ, Γ], is a free Abelian group with 2g generators. Thus the genus

Artin transfer (group theory) (28,815 words) [view diff] exact match in snippet view article

homomorphism from an arbitrary finite or infinite group to the commutator quotient group of a subgroup of finite index. Originally, such mappings arose as group

Riemannian connection on a surface (10,191 words) [view diff] exact match in snippet view article find links to article

to SO(3). Note that O(2) is the normaliser of SO(2) in SO(3) and the quotient group O(2)/SO(2), the so-called Weyl group, is a group of order 2 which acts

Adele ring (18,442 words) [view diff] exact match in snippet view article find links to article

I_{K}} are called principal ideles of I K . {\displaystyle I_{K}.} The quotient group C K := I K / K × {\displaystyle C_{K}:=I_{K}/K^{\times }} is called

Parabolic subgroup of a reflection group (3,742 words) [view diff] exact match in snippet view article find links to article

contains B. If furthermore G has a (B, N) pair, then the associated quotient group W = B / ( B ∩ N ) {\displaystyle W=B/(B\cap N)} is a Coxeter group,