Weakly G K -Perfect and Integral Closure of Ideals

Let R be a commutative Noetherian ring, K a nonzero finitely generated suitable R-module, and I an ideal of R. It is shown that if (R, ) is local, then  is G _K -perfect if and only if K is a canonical module for R. Furthermore, if I is integrally closed and G _K  ? dim _R I < ∞, then K _ is a canonical R _-module for every  ? Ass _R R/I whenever K satisfies Serre's condition (S ₁) or grade _K I > 0. Finally, it is shown that if CM ? dim _R I < ∞, then R _ is Cohen–Macaulay for every  ? Ass _R R/I.     

Hecke Algebras of Classical Groups over p-adic Fields II

In the previous part of this paper, we constructed a large family of Hecke algebras on some classical groups G defined over p-adic fields in order to understand their admissible representations. Each Hecke algebra is associated to a pair (J , ) of an open compact subgroup J and its irreducible representation which is constructed from given data = (, P₀, ). Here, is a semisimple element in the Lie algebra of G, P₀ is a parahoric subgroup in the centralizer of in G, and is a cuspidal representation on the finite reductive quotient of P₀. In this paper, we explicitly describe those Hecke algebras when P₀ is a minimal parahoric subgroup, is trivial and is a character.     

p-Typical Dynamical Systems and Formal Groups

By using the idea of logarithm, we give an effective method to decide whether a stable series is an endomorphism of a formal group or not. We also give examples that contradict Lubin's conjecture.     

Gaussian Estimates for Random Walks on Some Unimodular p-adic Groups

It is shown in this paper that the transition kernels corresponding to simple random walks on certain unimodular solvable p-adic groups admit upper Gaussian estimates.      

Remarks on the Transfer Factors for Unipotent Orbital Integrals in p-adic Classical Split Groups

This article studies unipotent orbital integrals on symplectic and orthogonal groups from the point of view of endoscopy. It begins by partitioning stable unipotent classes into packets and goes on to propose a transfer of these packets. It then discusses (in rough form) the associated transfer factors. Some supporting calculations in split odd orthogonal groups are given.     

On the p-Length of a Product of Two Schmidt Groups

It is established that a finite p-solvable group presenting the product of two of its Schmidt subgroups has p-length at most 2.     

Ranks of q-Ary 1-Perfect Codes

The rank of a q-ary code C of length n, r(C), isthe dimension of the subspace spanned by C. We establish the existence of q-ary 1-perfectcodes of length for m 4 and r(C)= n – m + s for each s {1,,m}. This is a generalization of the binary case proved by Etzion and Vardy in[4].     

Subgroups and Hulls of Specker Lattice-Ordered Groups

In this article, it will be shown that every -subgroup of a Specker -group has singular elements and that the class of -groups that are -subgroups of Specker -group form a torsion class. Methods of adjoining units and bases to Specker -groups are then studied with respect to the generalized Boolean algebra of singular elements, as is the strongly projectable hull of a Specker -group.     

On a Class of Supersoluble Groups

This paper identifies a class of supersoluble groups, called finitely generated hallsoging groups. The main result states that the product of a normal finitely generated hall-soging subgroup and a subnormal supersoluble subgroup is always supersoluble.AMS Subject Classification (1991): 20F16, 20F19, 20E25.     

A Group Theoretical Characterisation of S-Arithmetic Groups in Higher Rank Semi-Simple Groups

We give a characterisations for an abstract group to be an S-arithmetic group of a higher rank semi-simple group.     

Modular Representation Theory of Blocks with Trivial Intersection Defect Groups

We show that Uno's refinement of the projective conjecture of Dade holds for every block whose defect groups intersect trivially modulo the maximal normal p-subgroup. This corresponds to the block having p-local rank one as defined by Jianbei An and Eaton. An immediate consequence is that Dade's projective conjecture, Robinson's conjecture, Alperin's weight conjecture, the Isaacs–Navarro conjecture, the Alperin–McKay conjecture and Puig's nilpotent block conjecture hold for all trivial intersection blocks. Presented by A. Verschoren Mathematics Subject Classification (2000) Primary 20C20. Charles W. Eaton: Current address: School of Mathematics, University of Manchester, Sackville Street, PO Box 88, Manchester M60 1QC, U.K. e-mail: charles.eaton@manchester.ac.uk This research was supported in part by the Marsden Fund of New Zealand via grant #9144/3368248.     

Finite groups with seminormal Sylow subgroups

In this paper, we prove the following theorem： Let p be a prime number, P a Sylow psubgroup of a group G and π = π（G） ／ {p}. If P is seminormal in G, then the following statements hold： 1） G is a p-soluble group and P＇ ≤ Op（G）; 2） lp（G） ≤ 2 and lπ（G） ≤ 2; 3） if a π-Hall subgroup of G is q-supersoluble for some q ∈ π, then G is q-supersoluble.     

The L p -curvature images of convex bodies and L p -projection bodies

Associated with the L _p -curvature image defined by Lutwak, some inequalities for extended mixed p-affine surface areas of convex bodies and the support functions of L _p -projection bodies are established. As a natural extension of a result due to Lutwak, an L _p -type affine isoperimetric inequality, whose special cases are L _p -Busemann-Petty centroid inequality and L _p -affine projection inequality, respectively, is established. Some L _p -mixed volume inequalities involving L _p -projection bodies are also established.     

Computations of K- and L-Theory of Cocompact Planar Groups

The verification of the isomorphism conjectures of Baum and Connes and Farrell and Jones for certain classes of groups is used to compute the algebraic K- and L-theory and the topological K-theory of cocompact planar groups (=cocompact N.E.C-groups) and of groups G appearing in an extension where is a finite group and the conjugation -action on ⁿ is free outside . These computations apply, for instance, to two-dimensional crystallographic groups and cocompact Fuchsian groups.     

Character Values of Finite Groups

The aim of this paper is to describe simple methods to distribute the ordinary irreducible characters of finite groups into p-blocks and calculate the other character values from part of the values of the ordinary irreducible characters for p-blocks.2000 Mathematics Subject Classification: 20C20     

Algebraic K-Theory of Two-Dimensional Crystallographic Groups

Abstract. We explicitly compute the lower algebraicK-groups of the two-dimensional crystallographic groups.     

Solutions of Schrödinger Equations on Compact Lie Groups via Probabilistic Methods

By means of probabilistic methods global solutions of Schrödinger equations on compact connected semisimple Lie groups are constructed. The potentials and initial conditions are taken from the algebra of trigonometric polynomials. For these the solutions exist in the L ²-sense and pointwise.     

K1 of Some Non-Commutative Completed Group Rings

We compute K₁ of completed group rings of some two dimensional p-adic Lie groups. Dedicated to Professor Spencer Bloch on his sixtieth birthday