We consider Noether’s problem on the noncommutative rational functions invariant under a linear action of finite group. For abelian groups skew-fields are always rational, for solvable group they if is well-behaved – given by so-called complete representation. determine that admit such representations and call them totally pseudo-unramified. show skew-field finitely generated. Finally we study ...

A finite group all of whose complex character values are rational is called a group. In this paper, we classify groups degree graphs disconnected.

In this paper, I describe the structure of the biset functor B sending a p-group P to the group of units of its Burnside ring B(P ). In particular, I show that B is a rational biset functor. It follows that if P is a p-group, the structure of B(P ) can be read from a genetic basis of P : the group B(P ) is an elementary abelian 2-group of rank equal to the number isomorphism classes of rational...

streptococcuscus beta hemolytic group a is the most important pathogen causing which may lead to purulent and non purulent angina. rheumatic fever is the most important complication that is the cause of 30% to 40% of cardiac disease and disablement. this study was performed to evaluate prevalence of streptococcuscus beta hemolytic group a and estimate role of clinical findings in children with ...

The main goal of this paper is to propose a new practical method for hydrologic soil group estimation in surface runoff process based on geomorphology facieses and slop. The determination of CN based on this method can reduce the time and cost of project. In this research the upstream rivers of Glinak Watershed have been used as a case study to examine the efficiency of proposed method with a c...

the mordell-weil theorem states that the group of rational points‎ ‎on an elliptic curve over the rational numbers is a finitely‎ ‎generated abelian group‎. ‎in our previous paper, h‎. ‎daghigh‎, ‎and s‎. ‎didari‎, on the elliptic curves of the form $ y^2=x^3-3px$‎, ‎‎bull‎. ‎iranian math‎. ‎soc‎.‎‎ 40 (2014)‎, no‎. ‎5‎, ‎1119--1133‎.‎, ‎using selmer groups‎, ‎we have shown that for a prime $p$...

The Euler characteristic of all the Chow varieties, of a fixed projective variety, can be collected in a formal power series called the Euler-Chow series. This series coincides with the Hilbert series when the Picard group is a finite generated free abelian group. It is an interesting open problem to find for which varieties this series is rational. A few cases have been computed, and it is sus...

Let p be a polynomial in one complex variable. Smale’s mean value conjecture estimates |p′(z)| in terms of the gradient of a chord from (z, p(z)) to some stationary point on the graph of p. The conjecture does not immediately generalise to rational maps since its formulation is invariant under the group of affine maps, not the full Möbius group. Here we give two possible generalisations to rati...

We study a variant of the inverse problem of Galois theory and Abhyankar’s conjecture. If p is an odd rational prime and G is a finite p-group generated by s elements, s minimal, does there exist a normal extension L/Q such that Gal (L/Q) ∼= G with at most s rational primes that ramify in L? Given a nilpotent group of odd order G with s generators, we obtain a Galois extension L/Q with precisel...

Examples of projective homogeneous varieties over the field of Laurent series over p-adic fields which admit zero cycles of degree one and which do not have rational points are constructed. Let k be a field and X a quasi-projective variety over k. Let Z0(X) denote the group of zero cycles on X and deg : Z0(X) → Z the degree homomorphism which associates to a closed point x of X, the degree [k(x...