abelian group in Germany

Abelian group [əbiːliəngruːp]Math abelsche Gruppe

Sentence patterns related to "abelian group"

1. Every subgroup of a free abelian group is itself a free abelian group.

2. A torsion abelian group is an abelian group in which every element has finite order.

3. By the Fundamental Theorem of Finite Abelian Groups, every Abelian group of order 144 is isomorphic to the direct product of an Abelian group of order 16 = 24 and an Abelian group of

4. Every abelian group is a T-group.

5. Usually E is an additive abelian group.

6. All subgroups of an Abelian group are normal.

7. Every subgroup of an abelian group is abelian.

Jede Untergruppe einer abelschen Gruppe ist wieder abelsch.

8. A finitely generated torsion-free abelian group is free.

9. Abelian group: a group whose binary operation is commutative.

10. Abelian group 1 Abelian group In abstract algebra, an Abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not depend on their order (the axiom of commutativity).

11. Every abelian group can be embedded in a divisible group.

12. For example, the conjugacy classes of an Abelian group consist of singleton sets (sets containing one element), and every subgroup of an Abelian group is normal.

13. If 0=1, (1)-(3) are the axioms for an abelian group.

14. All cyclic groups are Abelian, but an Abelian group is not necessarily cyclic

15. Pertaining to an algebraic system in which an operation is commutative: an Abelian group

16. An Abelian group A A is a free Abelian group of rank r r if there exist u1,,ur ∈ A u 1,, u r ∈ A such that A = ⟨u1,,.ur⟩ A = ⟨ u 1,,

17. Abelian definition: of or relating to an Abelian group Meaning, pronunciation, translations and examples

18. A definition of an Abelian group is provided along with examples using matrix groups

19. The smallest non-abelian group is the symmetric group S3 which has 3! = 6 elements.

Die kleinste nichtabelsche Gruppe ist übrigens die symmetrische Gruppe S3 mit sechs Elementen.

20. The group F ab (S) is called the free Abelian group generated by the set S

21. Every subgroup and factor group of a finitely generated abelian group is again finitely generated abelian.

Jede Untergruppe und Faktorgruppe einer endlich erzeugten abelschen Gruppe ist wieder endlich erzeugt abelsch.

22. Generally speaking, negation is an automorphism of any abelian group, but not of a ring or field.

23. Any direct sum of finitely many finitely generated abelian groups is again a finitely generated abelian group.

Jede direkte Summe von endlich vielen endlich erzeugten abelschen Gruppen ist wieder eine endlich erzeugte abelsche Gruppe.

24. Its recurrent configurations form an Abelian group, whose identity is a fractal composed of self-similar patches.

25. A divisor D is an element of the free abelian group on the points of the surface.

26. As a simple corollary of the second statement is that every complex irreducible representation of an Abelian group is one-dimensional.

Ein einfaches Korollar des Lemmas von Schur ist, dass jede komplexe irreduzible Darstellung einer abelschen Gruppe eindimensional sein muss.

27. Abelian groups 1 Definition An Abelian group is a set A with a binary operation satisfying the following conditions: (A1) For

28. The abelian group of translations is a normal subgroup, while the Lorentz group is also a subgroup, the stabilizer of the origin.

29. If C is a preadditive category, then every morphism set Mor(X,Y) is an abelian group and therefore has a zero element.

30. The dual group of a locally compact abelian group is used as the underlying space for an abstract version of the Fourier transform.

31. BS(1, 1) is the free abelian group on two generators, and BS(1, −1) is the fundamental group of the Klein bottle.

32. Certain abelian group structures had been used implicitly in Carl Friedrich Gauss' number-theoretical work Disquisitiones Arithmeticae (1798), and more explicitly by Leopold Kronecker.

33. A countable periodic reduced abelian group is determined uniquely up to isomorphism by its Ulm invariants for all prime numbers p and countable ordinals α.

34. The (first) Ulm subgroup of an abelian group A, denoted U(A) or A1, is pωA = ∩n pnA, where ω is the smallest infinite ordinal.

35. The category of abelian groups is the fundamental example of an abelian category, and accordingly every subgroup of an abelian group is a normal subgroup.

36. An Abelian group is a group for which the elements commute (i.e., for all elements and). Abelian groups therefore correspond to groups with symmetric multiplication tables

37. (S) is an Abelian group with addition defined by ￿ x∈S k xx+ ￿ x∈S l xx := ￿ x∈S (k x +l x)x 9.7 Definition

38. The Nielsen–Schreier theorem is a non-abelian analogue of an older result of Richard Dedekind, that every subgroup of a free abelian group is free abelian.

39. In mathematics, a Witt group of a field, named after Ernst Witt, is an abelian group whose elements are represented by symmetric bilinear forms over the field.

40. The prize citation highlighted their work on stationary measures and closed orbits for non-abelian group actions on homogeneous spaces, solving a long-standing conjecture of Hillel Furstenberg.

In der Laudatio wurde ihre spektakuläre Arbeit über stationäre Maße und geschlossene Orbiten für Wirkungen nichtabelscher Gruppen auf homogenen Räumen hervorgehoben und speziell ihr Beweis einer Vermutung von Hillel Fürstenberg.

41. ‘Although Euler's work is, of course, not stated in group theoretic terms he does provide an example of the decomposition of an abelian group into Cosets of a subgroup.’

42. The Witt group of k is the abelian group W(k) of equivalence classes of non-degenerate symmetric bilinear forms, with the group operation corresponding to the orthogonal direct sum of forms.

43. Abelian groups 1 Definition An Abelian group is a set A with a binary operation satisfying the following conditions: (A1) For all a;b;c 2A, we have a (b c) = (a b) c (the associative law)

44. In mathematics, the Mordell–Weil theorem states that for an abelian variety A over a number field K, the group A(K) of K-rational points of A is a finitely-generated abelian group, called the Mordell-Weil group.

45. The fundamental theorem of finite Abelian groups states that a finite Abelian group is isomorphic to a direct product of cyclic groups of prime-power order, where the decomposition is unique up to the order in which the factors are written.

46. Definition of Abelian : commutative sense 2 Abelian group Abelian ring Examples of Abelian in a Sentence Recent Examples on the Web Microsoft is trying to chase a new quantum computer based on a new topography and a yet-undiscovered particle called non-Abelian anyons.

47. Formally, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point O. An elliptic curve is an abelian variety – that is, it has a multiplication defined algebraically, with respect to which it is an abelian group – and O serves as the identity element.