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941.
It is known that the subgroup growth of finitely generated linear groups is either polynomial or at least $n^{\frac{{\log n}}{{\log \log n}}} $ . In this paper we prove the existence of a finitely generated group whose subgroup growth is of type $n^{\frac{{\log n}}{{(\log \log n)^2 }}} $ . This is the slowest non-polynomial subgroup growth obtained so far for finitely generated groups. The subgroup growth typen logn is also realized. The proofs involve analysis of the subgroup structure of finite alternating groups and finite simple groups in general. For example, we show there is an absolute constantc such that, ifT is any finite simple group, thenT has at mostn c logn subgroups of indexn. 相似文献
942.
Gábor Tardos 《Inventiones Mathematicae》1996,123(1):95-104
The Hanna Neumann conjecture states that the intersection of two nontrivial subgroups of rankk+1 andl+1 of a free group has rank at mostkl+1. In a recent paper [3] W. Dicks proved that a strengthened form of this conjecture is equivalent to his amalgamated graph conjecture. He used this equivalence to reprove all known upper bounds on the rank of the intersection. We use his method to improve these bounds. In particular we prove an upper bound of 2kl–k–l+1 for the rank of the intersection above (k,l2) improving the earlier 2kl-min(k, l) bound of [1].We prove a special case of the amalgamated graph conjecture in the hope that it may lead to a proof of the general case and thus of the strengthened Hanna Neumann conjecture.Oblatum 6-II-1995 & 19-VI-1995Supported by the NSF grants No. CCR-92-00788 CCR-95-03254 and the (Hungarian) National Scientific Research Fund (OTKA) grant No. F014919. The author was visiting the Computation and Automation Institute of the Hungarian Academy of Sciences while part of this research was done. 相似文献
943.
We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416. 相似文献
944.
For everyt>1 and positiven we construct explicit examples of graphsG with |V (G)|=n, |E(G)|c
t
·n
2–1/t
which do not contain a complete bipartite graghK
t,t
!+1 This establishes the exact order of magnitude of the Turán numbers ex (n, K
t,s
) for any fixedt and allst!+1, improving over the previous probabilistic lower bounds for such pairs (t, s). The construction relies on elementary facts from commutative algebra.Research supported in part by NSF Grants DMS-8707320 and DMS-9102866.Research supported in part by Hungarian National Foundation for Scientific Research Grant 相似文献
945.
946.
947.
948.
949.
A completely automated method to determine the most common parameters in cured meat products is proposed. The approach to full automation is based on the coupling of a robotic station for development of preliminary operations (namely weighing of the sample, grinding, leaching, filtration and transport to the aspiration zone) and a continuous unsegmented manifold for derivatisation and spectrophotometric monitoring of the reaction coloured products. This assembly works in an unattended fashion thus eliminating the bottleneck produced by the determination of these parameters in routine laboratories. The good agreement between results obtained by the proposed method and those from conventional methods for target analytes confirms its excellent performance and usefulness. 相似文献
950.
The complex (1) has been prepared and its structure determined. Complex1 is the first stable thioether derivative of a metal carbonyl containing only cobalt as metal. It crystallizes in the monoclinic P21/c space group, witha = 13.975( 4 ),b = 11.363( 3 ),c = 14.686(2)A, = 112.25(2)°,V = 2158.5(7)A3.Z = 4. The solution using direct methods and the anisotropic refinement of all nonhydrogen atoms led toR = 0.039,wR = 0.041 for 3296 reflections with F> 4.0(F) Analogous but less stable complexes are formed with 1,6-diphenyl-2,5-dithiahexane and the crown thioether 1,4,7-trithiacyclonane, the latter functioning either as a bidenlate or a tridentate ligand. 相似文献