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1.
P. R. Hewitt 《Proceedings of the American Mathematical Society》1998,126(7):1909-1914
Let be a group, let be a field, and let be a local system - an upwardly directed collection of subgroups whose union is . In this paper we give a short, elementary proof of the following result: If either is a --bimodule, or else is finite dimensional over its center, then . From this we deduce as easy corollaries some recent results of Meierfrankenfeld and Wehrfritz on the cohomology of a finitary module.
2.
If is a perfect field of characteristic , we show that the Quillen K-groups are uniquely -divisible for . In fact, the Milnor K-groups are uniquely -divisible for all . This implies that is -connected after profinite completion for a complete discrete valuation ring with perfect residue field.
3.
4.
G. Androulakis 《Proceedings of the American Mathematical Society》1998,126(5):1425-1428
We give an example of a compact metric space , an open dense subset of , and a sequence in which is pointwise convergent to a non-continuous function on , such that for every there exists with for all , yet is equivalent to the unit vector basis of the James quasi-reflexive space of order 1. Thus does not embed isomorphically in the closed linear span of . This answers in the negative a question asked by H. Haydon, E. Odell and H. Rosenthal.
5.
Sen-Zhong Huang Jan van Neerven Frank Rä biger 《Proceedings of the American Mathematical Society》1998,126(5):1397-1407
Let be a locally compact abelian group. A function is said to be a weight if it is locally bounded, Borel measurable and submultiplicative. We call a weight on semi-bounded if there exist a constant and a subsemigroup with such that
for all Using functional analytic methods, we show that all Beurling algebras whose defining weight is semi-bounded satisfy Ditkin's condition.
6.
Luis Guijarro 《Proceedings of the American Mathematical Society》1998,126(5):1541-1545
The soul theorem states that any open Riemannian manifold with nonnegative sectional curvature contains a totally geodesic compact submanifold such that is diffeomorphic to the normal bundle of . In this paper we show how to modify into a new metric so that:
- has nonnegative sectional curvature and soul .
- The normal exponential map of is a diffeomorphism.
- splits as a product outside of a compact set.
7.
Michel Brion 《Proceedings of the American Mathematical Society》1998,126(9):2535-2539
Let be a smooth affine algebraic variety where a reductive algebraic group acts with a smooth quotient space . We show that the algebraic differential forms on which are pull-backs of forms on are exactly the -invariant horizontal differential forms on .
8.
Humio Ichimura 《Proceedings of the American Mathematical Society》1998,126(5):1315-1320
For any totally real number field and any prime number , Greenberg's conjecture for asserts that the Iwasawa invariants and are both zero. For a fixed real abelian field , we prove that the conjecture is ``affirmative' for infinitely many (which split in if we assume the abc conjecture for .
9.
A Borsuk theorem for antipodal links and a spectral characterization of linklessly embeddable graphs
Lá szló Lová sz Alexander Schrijver 《Proceedings of the American Mathematical Society》1998,126(5):1275-1285
For any undirected graph , let be the graph parameter introduced by Colin de Verdière. In this paper we show that if and only if is linklessly embeddable (in ). This forms a spectral characterization of linklessly embeddable graphs, and was conjectured by Robertson, Seymour, and Thomas. A key ingredient is a Borsuk-type theorem on the existence of a pair of antipodal linked -spheres in certain mappings . This result might be of interest in its own right. We also derive that for each linklessly embeddable graph , where is the graph parameter introduced by van der Holst, Laurent, and Schrijver. (It is the largest dimension of any subspace of such that for each nonzero , the positive support of induces a nonempty connected subgraph of .)
10.
Gabriel Navarro 《Proceedings of the American Mathematical Society》1998,126(1):65-66
Suppose that is a Sylow -subgroup of a finite -solvable group . If , then the number of -conjugates of in can be read off from the character table of .
11.
Victoria Paolantoni 《Proceedings of the American Mathematical Society》1998,126(6):1733-1738
Let be a smooth real hypersurface of and a compact submanifold of . We generalize a result of A. Boggess and R. Dwilewicz giving, under some geometric conditions on and , an estimate of the submeanvalue on of any function on a neighbourhood of , by the norm of on a neighbourhood of in .
12.
Aner Shalev 《Proceedings of the American Mathematical Society》1998,126(12):3495-3499
Let be a residually finite torsion group. We show that, if has a finite 2-subgroup whose centralizer is finite, then is locally finite. We also show that, if has no -torsion, and is a finite 2-group acting on in such a way that the centralizer is soluble, or of finite exponent, then is locally finite.
13.
J. Ding 《Proceedings of the American Mathematical Society》1998,126(5):1355-1361
We present some results on the point spectrum of the Frobenius-Perron operator and the Koopman operator associated with a nonsingular transformation on a -finite measure space .
14.
Tadashi Yanai 《Proceedings of the American Mathematical Society》1998,126(8):2221-2228
In this paper, we prove the following two results which generalize the theorem concerning automorphic-differential endomorphisms asserted by J. Bergen. Let be a ring, its left Martindale quotient ring and a right ideal of having no nonzero left annihilator. (1) Let be a pointed coalgebra which measures such that the group-like elements of act as automorphisms of . If is prime and for , then . Furthermore, if the action of extends to and if such that , then . (2) Let be an endomorphism of given as a sum of composition maps of left multiplications, right multiplications, automorphisms and skew-derivations. If is semiprime and , then .
15.
Dave Witte 《Proceedings of the American Mathematical Society》1998,126(4):1005-1015
Let and be matrices of determinant over a field , with or . We show that if is not a scalar matrix, then is a product of matrices similar to . Analogously, we conjecture that if and are elements of a semisimple algebraic group over a field of characteristic zero, and if there is no normal subgroup of containing but not , then is a product of conjugates of . The conjecture is verified for orthogonal groups and symplectic groups, and for all semisimple groups over local fields. Thus, in a connected, semisimple Lie group with finite center, the only conjugation-invariant subsemigroups are the normal subgroups.
16.
Gary L. Peterson 《Proceedings of the American Mathematical Society》1998,126(7):1897-1900
Suppose and are endomorphism near-rings generated by
groups of automorphisms containing the inner automorphisms of two respective finite perfect groups and . In this note we show that if and are isomorphic, then and are isomorphic.
groups of automorphisms containing the inner automorphisms of two respective finite perfect groups and . In this note we show that if and are isomorphic, then and are isomorphic.
17.
Chih-Nung Hsu 《Proceedings of the American Mathematical Society》1998,126(7):1955-1961
Let be a global function field, a degree one prime divisor of and let be the Dedekind domain of functions in regular outside . Let be the Hilbert class field of , the integral closure of in . Let be a rank one normalized Drinfeld -module and let be a prime ideal in . We explicitly determine the finite -module structure of . In particular, if , is an odd prime number and is the Carlitz -module, then the finite -module is always cyclic.
18.
A. Skopenkov 《Proceedings of the American Mathematical Society》1998,126(8):2467-2476
For a space let . Let act on and on by exchanging factors and antipodes respectively. We present a new short proof of the following theorem by Weber: For an -polyhedron and , if there exists an equivariant map , then is embeddable in . We also prove this theorem for a peanian continuum and . We prove that the theorem is not true for the 3-adic solenoid and .
19.
Let be a polynomial of degree having only real zeros and none in . We look for a sharp upper bound for at an arbitrary point of the complex plane in terms of the supremum norm on .
20.
Marí a J. Gonzá lez 《Proceedings of the American Mathematical Society》1998,126(5):1429-1431
Let be a Fuchsian group. We show that the existence of a set on with no -equivalent points and positive logarithmic capacity does not imply that is of convergence type.