Algebraisierung Scharf 2-Fach Transitiver Permutationsmengen durch Quasibereiche

Sharply 2-transitive permutation sets (M,) with the property: every which interchanges two distinct elements of M is in and V (where := { ; ²=id }) can be characterized algebraically by quasi-domains as defined by G. Kist.Among other examples there are some which show that a sharply 2-transitive permutation set (M,) is not necessarily a group a neither if (M,) satisfies (R^*): id and (, ^–1 ) which answers a question of H. Karzel [7], nor if (M,) is symmetric (contrary to the case of a symmetric sharply 3-transitive permutation set (M,) where is always a group [8]).

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Herrn Rafael Artzy zum 70. Geburtstag     

On Locally Projective Graphs of Girth 5

Let be a graph and G be a 2-arc transitive automorphism group of . For a vertex x let G(x)^(x) denote the permutation group induced by the stabilizer G(x) of x in G on the set (x) of vertices adjacent to x in . Then is said to be a locally projective graph of type (n,q) if G(x)^(x) contains PSL_n(q) as a normal subgroup in its natural doubly transitive action. Suppose that is a locally projective graph of type (n,q), for some n 3, whose girth (that is, the length of a shortest cycle) is 5 and suppose that G(x) acts faithfully on (x). (The case of unfaithful action was completely settled earlier.) We show that under these conditions either n=4, q=2, has 506 vertices and , and contains the Wells graph on 32 vertices as a subgraph. In the latter case if, for a given n, at least one graph satisfying the conditions exists then there is a universal graph W(n) of which all other graphs for this n are quotients. The graph W(3) satisfies the conditions and has 2²⁰ vertices.     

K-theory of fine topological algebras, Chern character, and assembly

TheK-theory of the group algebra [] for a countable, discrete group is defined in terms of the simplicial ring of smooth simplices on [], where [] is given the fine topology with respect to its finite-dimensional, linear subspaces. The assembly map for this theory :K _* B K _* [] is studied and shown to be a rational injection. The proof uses the Connes-Karoubi Chern character fromK-theory of Banach algebras to cyclic homology, here generalized to any fine topological algebra, and proved to be multiplicative.     

K-theory of reduced C*-algebras and rapidly decreasing functions on groups

We associate to any length function L on a group a space of rapidly decreasing functions on (in the l ² sense), denoted by H _L (). When H _L () is contained in the reduced C*-algebra C _r ^* () of (), then it is a dense *-subalgebra of C _r ^* () and we prove a theorem of A. Connes which asserts that under this hypothesis H _L () has the same K-theory as C _r ^* (). We introduce another space of rapidly decreasing functions on (in the l ¹ sense), denoted by H _L ^1, (), which is always a dense *-subalgebra of the Banach algebra l ¹(), and we show that H _L ^1, () has the same K-theory as l ¹().     

Mortality of iterated Gallai graphs

For a finite or infinite graphG, theGallai graph (G) ofG is defined as the graph whose vertex set is the edge setE(G) ofG; two distinct edges ofG are adjacent in (G) if they are incident but do not span a triangle inG. For any positive integert, thetth iterated Gallai graph ^t (G) ofG is defined by ( ^t–1(G)), where ⁰(G):=G. A graph is said to beGallai-mortal if some of its iterated Gallai graphs finally equals the empty graph. In this paper we characterize Gallai-mortal graphs in several ways.     

Bases for Splines on a Subdivided Domain

Let S^r() be the module of all splines of smoothness r on the rectilinear partition which subdivides some domain D. Further, let S^r() be the module of all splines of smoothness r on which also subdivides D, where is a finer subdivision of . We study the relationship between a generating set of S^r() and a generating set for S^r(). This paper gives an algorithm for extending a generating set for S^r() to one for for S^r(). This method is built on algebraic properties of splines and the Gröbner Basis Algorithm.     

On Distance-Regular Graphs with Height Two

Let be a distance-regular graph with diameter at least three and height h = 2, where . Suppose that for every in and in _d(), the induced subgraph on _d() ₂() is a clique. Then is isomorphic to the Johnson graph J(8, 3).     

Bounding the diameter of a distance regular graph by a function ofk d

Let be a distance regular graph with diameterd, and _d () the set of vertices at distanced from. is said to be thin if the induced subgraph on _d () is a union of cliques for every vertex. We show that the diameterd is bounded above by a function depending only onk _d, which is the cardinality of _d (), if is not thin. We also investigate thin distance regular graphs witha _d 0.     

Bipartite <Emphasis Type="Italic">Q</Emphasis>-Polynomial Distance-Regular Graphs

Let denote a bipartite distance-regular graph with diameter D12. We show is Q-polynomial if and only if one of the following (i)–(iv) holds: (i) is the ordinary 2D-cycle. (ii) is the Hamming cube H(D,2). (iii) is the antipodal quotient of H(2D,2). (iv) The intersection numbers of satisfy where q is an integer at least 2. We obtain the above result using the Terwilliger algebra of .AMS 1991 Subject Classification: Primary 05E30Final version received: April 10, 2003     

Convexity theories III. Classification of certain real convexity theories

In this paper we classify all real convexity theories that contain the standard convexity theory _c. For this purpose we consider three subcases: finitary; infinitary and (_sc\_c)Ø; infinitary and _sc=_c. In each of these subcases one encounters a phenomenon resembling bifurcation.This research was supported by the Deutsche Forschungsgemeinschaft.     

On the Operator Semirings of a Γ-Semiring

In this paper we introduce the notion of operator semirings of a -semiring to study -semirings. It is shown that the lattices of all left (right) ideals (two-sided ideals) of a -semiring and its right (respectively left) operator semiring are isomorphic. This has many applications to characterize various -semirings.AMS Subject Classification (2000): 16Y60, 16Y99     

Subgroups of the general symplectic group containing the group of diagonal matrices

There are described the subgroups of the general symplectic group =GSp(2n, R) over a commutative semilocal ring R, containing the group of symplectic diagonal matrices. For each such subgroup P there is uniquely defined a symplectic D-net a such that ()pN(), where () is the net subgroup in corresponding to (cf. RZhMat, 1977, 5A288), and N() is its normalizer. The quotient group N × ()/() is calculated. There are also considered subgroups in Sp(2n, R). Analogous results for subgroups of the general linear group were obtained earlier in RZhMat, 1978, 9A237.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 103, pp. 31–47, 1980.     

On the removable singularities of CR functions given on a generic manifold

Summary In this paper we consider the problem of holomorphic continuation and removal of singularities of the CR functions given on K, where is a generic manifold with nondegenerate Levi form and K is a meromorphically p-convex compactum. We get some conditions on , relative to p-convexity and q-concavity, under which every integrable CR function given on K extends holomorphically in some domain \K, where is a wedge domain with edge . Our Results are local.Authors had a support of Russian Fund of Fundamental Investigations (grant 93-011-258).     

Die Automorphismengruppen hyperelliptischer Kurven

Let be a hyperelliptic curve over an algebraically closed field of characteristic O and G a group of automorphisms of that contains the canonical involution of . We describe the group-theoretical structure of G by means of the arithmetical structure of the morphism ^G.     

Covering the Hecke Triangle Surfaces

In the mid-1980s an equivalence was established between the simple closed geodesics on the Riemann surfaces obtained as quotients of the upper half plane H by any of the following subgroups of the modular group (1) : , (3), and ³. An axis of a hyperbolic element of (1) projects to a simple closed geodesic on one of these surfaces if and only if it does so on the other two.This equivalence was used to obtain a variety of Diophantine and geometric results. In subsequent related investigations, the role of (1) was assumed by the Hecke triangle group G_q for q 3. (For q = 3, we have (1) = G₃.) These works employed the analog of ³, denoted _q.In the context of the G_q, the present paper gives the analog of , which we denote _q. As in the case q = 3, we have [_q:_q] = 2. A rather full discussion of geometry of _q\ H is given. In particular, we demonstrate that the equivalence of simple closed geodesics on _q\ H and _q\ H does not hold for q 7.As of this writing, we have not been able to obtain an appropriate analog of (3).     

On graphs and Lie rings

From a finite oriented graph , finite-dimensional graded nilpotent Lie rings () and () are naturally constructed; these rings are related to subtrees and connected subgraphs of , respectively. Diverse versions of these constructions are also suggested. Moreover, an embedding of Lie rings of the form () in the adjoint Lie rings of finite-dimensional associative rings (also determined by the graph ) is indicated.Translated from Matematicheskie Zametki, vol. 77, no. 3, 2005, pp. 449–459.Original Russian Text Copyright © 2005 by Yu. S. Sernenov.This revised version was published online in April 2005 with a corrected issue number.     

Superrigidity of lattices in solvable Lie groups

Summary Let be a closed, cocompact subgroup of a simply connected, solvable Lie groupG, such that Ad _G has the same Zariski closure as AdG. If : GL _n () is any finite-dimensional representation of , we show that virtually extends to a representation ofG. (By combining this with work of Margulis on lattices in semisimple groups, we obtain a similar result for lattices in many groups that are neither solvable nor semisimple.) Furthermore, we show that if is isomorphic to a closed, cocompact subgroup of another simply connected, solvable Lie groupG, then any isomorphism from to extends to a crossed isomorphism fromG toG. In the same vein, we prove a more concrete form of Mostow's theorem that compact solvmanifolds with isomorphic fundamental groups are diffeomorphic.Oblatum 5-VII-1994 & 15-IV-1995     

Geodesic Graphs with Constant Mean Curvature in Spheres

We study the existence and unicity of graphs with constant mean curvature in the Euclidean sphere of radius a. Given a compact domain , with some conditions, contained in a totally geodesic sphere S of and a real differentiable function on , we define the graph of in considering the height (x) on the minimizing geodesic joining the point x of to a fixed pole of . For a real number H such that |H| is bounded for a constant depending on the mean curvature of the boundary of and on a fixed number in (0,1), we prove that there exists a unique graph with constant mean curvature H and with boundary , whenever the diameter of is smaller than a constant depending on . If we have conditions on , that is, let be a graph over of a function, if |H| is bounded for a constant depending only on the mean curvature of and if the diameter of is smaller than a constant depending on H and , then we prove that there exists a unique graphs with mean curvature H and boundary . The existence of such a graphs is equivalent to assure the existence of the solution of a Dirichlet problem envolving a nonlinear elliptic operator.     

Free Algebras of Automorphic Forms on the Upper Half-Plane

We find all pairs (,a) consisting of a cocompact Fuchsian group of genus zero and an automorphy factor a of for which the graded algebra of a--automorphic forms is free.