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.     

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.     

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.     

Algebraic K-Theory of Two-Dimensional Crystallographic Groups

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

L-Fuzzy子格群的同态

证明了双诱导映射下L-Fuzzy子格群的像与逆像仍为L-Fuzzy子格群,基于L-Fuzzy集的层次结构特征,研究L-Fuzzy子格群的同态,给出了它们的性质.     

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.     

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.      

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.     

可除阿贝尔p-群的自同构群

主要探讨了秩大于或者等于p-1的可除阿贝尔p-群的p-自同构群,并且得到这些p-自同构如何作用在该可除阿贝尔p-群上.这些结论有助于进一步理解 ?ernikov p-群的结构.     

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.     

Groups with Many Rewritable Products

For any integer n ≥ 2, a group G is said to have the n-rewritable property R _n if every infinite subset X of G contains n elements x ₁,…, x _n such that the product x ₁…x _n  = x _σ(1)…x _σ(n) for some permutation σ ≠ 1. We show here that if G satisfies R _n , then G has a subgroup N of finite index with a finite central subgroup A of N such that the exponent of (N/A)/Z(N/A) is finite and has size bounded by (n ? 1)!. This extends the main result in [4 Curzio , M. , Longobardi , P. , Maj , M. , Rhemtulla , A. ( 1992 ). Groups with many rewritable products . Proc. AMS. 115 ( 4 ): 931 – 934 .[Crossref], [Web of Science ®] , [Google Scholar]] which asserts that a group G is an R _n group for some integer n if and only if G has a normal subgroup F such that G/F is finite, F is an FC-group, and the exponent of F/Z(F) is finite.     

Nielsen Methods and Groups Acting on Hyperbolic Spaces

We show that for any n & in there exists a constant C(n) such that any n-generated group G which acts by isometries on a -hyperbolic space (with >0) is either free or has a nontrivial element with translation length at most C(n).     

On Primary Abelian Groups Modulo Finite Subgroups

We study the existence of several classes 𝒦 of Abelian p-groups, p a fixed prime, which possess the following property: A ∈ 𝒦?A/F ∈ 𝒦, whenever F is a finite subgroup of the Abelian p-group A.     

On the Solvability of Finite Irreducible Linear Groups with Hall TI-Subgroups

Conditions for a -solvable complex linear group of a relatively small degree to be solvable are found.     

Approximately Linear Mappings in Banach Modules over a C^＊-algebra

Let X and Y be vector spaces. The authors show that a mapping f ： X →Y satisfies the functional equation 2d f（∑^2d j=1（-1）^j＋1xj/2d）=∑^2dj=1（-1）^j＋1f（xj） with f（0） = 0 if and only if the mapping f ： X→ Y is Cauchy additive, and prove the stability of the functional equation （≠） in Banach modules over a unital C^＊-algebra, and in Poisson Banach modules over a unital Poisson C＊-algebra. Let A and B be unital C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊- algebras. As an application, the authors show that every almost homomorphism h ： A →B of A into is a homomorphism when h（（2d-1）^nuy） =- h（（2d-1）^nu）h（y） or h（（2d-1）^nuoy） = h（（2d-1）^nu）oh（y） for all unitaries u ∈A, all y ∈ A, n = 0, 1, 2,.... Moreover, the authors prove the stability of homomorphisms in C^＊-algebras, Poisson C^＊-algebras or Poisson JC^＊-algebras.     

Linearity of Zp[[t]]-Perfect Groups

Let G be a _p[[t]]-standard group of level 1. Then G is _p[[t]]-perfect if its lower central series is given by powers of the maximal ideal (p, t), i.e. if _n(G) = G((p,t)ⁿ). We prove that a _p[[t]]-perfect group is linear by imitating the proof that a _p[[t]]-standard group is linear.     

Notes on Essentially Finitely Indecomposable Nonthick Primary Abelian Groups

Let R be a commutative Noetherian ring of prime characteristic and M be an x-divisible right R[x, f]-module that is Noetherian as R-module. We give an affirmative answer to the question of Sharp and Yoshino in the case where R is semilocal and prove that the set of graded annihilators of R[x, f]-homomorphic images of M is finite. We also give a counterexample in the general case.     

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.     

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.