multiplicative group वाक्य
उदाहरण वाक्य
मोबाइल
- All left-isoclinic rotations form a noncommutative subgroup S 3 L of SO ( 4 ), which is isomorphic to the multiplicative group S 3 of unit quaternions.
- The Artin reciprocity law, which is a high level generalisation of the Gauss quadratic reciprocity law, states that the product vanishes on the multiplicative group of the number field.
- The case of 2-cocycles for the multiplicative group is that of the Brauer group, and the implications seem to have been well known to algebraists of the 1930s.
- The "'Fiat Shamir heuristic "'is a technique in cryptography for taking an multiplicative groups of integers modulo n with prime " n ".
- Compare the values 6 and 4 for Euler's totient function, the multiplicative group of integers modulo n for " n " = 9 and 10, respectively.
- Thus the multiplicative group of non-zero quaternions acts by conjugation on the copy of "'R "'3 consisting of quaternions with real part equal to zero.
- In this way, the function mapping each triangle to its area or perimeter can be seen as equivariant for a multiplicative group action of the scaling transformations on the positive real numbers.
- This follows from the fact that belongs to the multiplicative group ( \ mathbb { Z } / m \ mathbb { Z } ) ?if and only if is coprime to.
- If the matrix entries come from a field, the scalar matrices form a group, under matrix multiplication, that is isomorphic to the multiplicative group of nonzero elements of the field.
- The connecting homomorphism from, which is simply the group of-valued points, to is essentially the spinor norm, because is isomorphic to the multiplicative group of the field modulo squares.
- So it will not be true that " any element in GF ( p ) [ x ] / f ( x ) other than the additive identity " will generate the multiplicative group.
- This can be phrased in the language of algebraic groups, in terms of the existence of a group action of an algebraic torus ( equivalently by a multiplicative group of torus embeddings ".
- The multiplicative group of " p "-adic units is a product of the finite group of roots of unity and a group isomorphic to the " p "-adic integers.
- It is a Noetherian ring if and only if there are finitely many square classes; that is, if the squares in " k " form a subgroup of finite index in the multiplicative group.
- But a finite group ( the multiplicative group of " D " in our case ) cannot be a union of conjugates of a proper subgroup; hence, " n " = 1.
- The ordinary exponential function of mathematical analysis is a special case of the exponential map when G is the multiplicative group of positive real numbers ( whose Lie algebra is the additive group of all real numbers ).
- Now we let the multiplicative group act on this interval by a multiplication of all its elements by a number g, resulting in gS being the interval with bounds g \ cdot a, g \ cdot b.
- Here " G " m ( the multiplicative group ) denotes the sheaf of invertible regular functions, and the shift [ " 1 ] means that this sheaf is viewed as a complex in degree 1.
- There are two kinds of spheres in the theory : those coming from the multiplicative group playing the role of the-sphere in topology, and those coming from the simplicial sphere ( considered as constant simplicial sheaf ).
- Formally, " g " is a group ( typically the multiplicative group of a finite field or an elliptic curve group ) and " x " and " y " are randomly chosen integers.
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