نتایج جستجو برای: group orders
تعداد نتایج: 1031820 فیلتر نتایج به سال:
The algebraic structure of groups is familiar to anyone who has studied abstract algebra. Familiar to anyone who has studied any mathematics is the concept of ordering, for example the standard less than or equal to with the integers. We can combine these structures to create a new hybrid algebraic structure. In the following, we will define exactly how order structures and group structures int...
For a given division algebra of the quaternions, we construct two types of units of its Z-orders: Pell units and Gauss units. Also, if K = Q √ −d, d ∈ Z \ {0, 1} is square free and R = IK , we classify R and G such that U1(RG) is hyperbolic. In particular, we prove that U1(RK8) is hyperbolic iff d > 0 and d ≡ 7 (mod 8). In this case, the hyperbolic boundary ∂(U1(RG)) ∼= S, the two dimensional s...
Factoring large integers into primes is one of the most important and most difficult problems of computational number theory (the twin problem is primality testing [13]). Trial division, Fermat's algorithm [1], [3], [8], Pollard's p-\ method [6], Williams' p + \ method [11], Lenstra's elliptic curve method (ECM) [5], Pomerance's quadratic sieve (QS) [7], [10], and Pollard's number field sieve (...
Generally Digital Signal Processing is Mathematical manipulation of the signals. The manipulation parameters may get differ from one technique to another. In this paper IIR Butterworth filters has been designed for various orders to analyze group delay. The developed IIR filters are designed and simulated using matlab with different filter orders. The simulated results shows that IIR filters wi...
Let E be a number field and G be a finite group. Let A be any OE-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case that the Wedderburn decomposition E[G] ∼= ⊕χMχ is explicitly computable and each Mχ is in fact a matrix ring over a field, this leads to an algorithm that eithe...
In 1989, the first subexponential algorithm for computing the class group of an imaginary quadratic order was introduced by Hafner and McCurley. Their algorithm is based on an integer factorization algorithm due to Seysen, and is conditional on the truth of the Extended Riemann Hypothesis. Not long after, their result was generalized to arbitrary algebraic number fields by Buchmann. Efficient v...
Given a prime p and a natural number n, we provide simple divisibility criterions that determine whether all solvable group of order n have a nontrivial normal psubgroup, or there is exactly one group of order n without nontrivial normal psubgroups.
Let G be an abelian group acting on a set X, and suppose that no element of G has any finite orbit of size greater than one. We show that every partial order on X invariant under G extends to a linear order on X also invariant under G. We then discuss extensions to linear preorders when the orbit condition is not met, and show that for any abelian group acting on a set X, there is a G-invariant...
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