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作者：Burness, Timothy C.; Guralnick, Robert M.; Harper, Scott
摘要：A group G is said to 3/2-generated if every nontrivial element belongs to a generating pair. It is easy to see that if G has this property, then every proper quotient of G is cyclic. In this paper we prove that the converse is true for finite groups, which settles a conjecture of Breuer, Guralnick and Kantor from 2008. In fact, we prove a much stronger result, which solves a problem posed by Brenner and Wiegold in 1975. Namely, if G is a finite group and every proper quotient of G is cyclic, t...
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作者：Fintzen, Jessica
摘要：Let k be a non-archimedean local field with residual characteristic p. Let G be a connected reductive group over k that splits over a tamely ramified field extension of k. Suppose p does not divide the order of the Weyl group of G. Then we show that every smooth irreducible complex representation of G(k) contains an .6-type of the form constructed by Kim-Yu and that every irreducible supercuspidal representation arises from Yu's construction. This improves an earlier result of Kim, which held ...
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作者：Heuts, Gijs
摘要：We consider a homotopy theory obtained from that of pointed spaces by inverting the maps inducing isomorphisms in v(n)-periodic homotopy groups. The case n = 0 corresponds to rational homotopy theory. In analogy with Quillen's results in the rational case, we prove that this v(n)-periodic homotopy theory is equivalent to the homotopy theory of Lie algebras in T(n)-local spectra. We also compare it to the homotopy theory of commutative coalgebras in T(n)-local spectra, where it turns out there ...
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作者：Brieussel, Jeremie; Zheng, Tianyi
摘要：We give a solution to the inverse problem (given a prescribed function, find a corresponding group) for large classes of speed, entropy, isoperimetric profile, return probability and L-p-compression functions of finitely generated groups. For smaller classes, we give solutions among solvable groups of exponential volume growth. As corollaries, we prove a recent conjecture of Amir on joint evaluation of speed and entropy exponents and we obtain a new proof of the existence of uncountably many p...
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作者：Alweiss, Ryan; Lovett, Shachar; Wu, Kewen; Zhang, Jiapeng
摘要：A sunflower with r petals is a collection of r sets so that the intersection of each pair is equal to the intersection of all of them. Erdos and Rado proved the sunflower lemma: for any fixed r, any family of sets of size w, with at least about w(w) sets, must contain a sunflower with r petals. The famous sunflower conjecture states that the bound on the number of sets can be improved to c(w) for some constant c. In this paper, we improve the bound to about (log w)(w). In fact, we prove the re...
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作者：Li, Chao; Liu, Yifeng
摘要：In this article, we study the Chow group of the motive associated to a tempered global L-packet pi of unitary groups of even rank with respect to a CM extension, whose global root number is -1. We show that, under some restrictions on the ramification of pi, if the central derivative L'(1/2, pi) is nonvanishing, then the pi-nearly isotypic localization of the Chow group of a certain unitary Shimura variety over its reflex field does not vanish. This proves part of the Beilinson-Bloch conjectur...
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作者：Aspero, David; Schindler, Ralf
摘要：We show that Martin's Maximum(++) implies Woodin's P-max axiom (*). This answers a question from the 1990s and amalgamates two prominent axioms of set theory which were both known to imply that there are aleph(2) many real numbers.
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作者：Leuzinger, Enrico; Young, Robert
摘要：The Dehn function and its higher-dimensional generalizations measure the difficulty of filling a sphere in a space by a ball. In nonpositively curved spaces, one can construct fillings using geodesics, but fillings become more complicated in subsets of nonpositively curved spaces, such as lattices in symmetric spaces. In this paper, we prove sharp filling inequalities for (arithmetic) lattices in higher rank semisimple Lie groups. When n is less than the rank of the associated symmetric space,...
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作者：Elgindi, Tarek M.
摘要：It has been known since work of Lichtenstein and Gunther in the 1920s that the 3D incompressible Euler equation is locally well-posed in the class of velocity fields with Ho center dot lder continuous gradient and suitable decay at infinity. It is shown here that these local solutions can develop singularities in finite time, even for some of the simplest three-dimensional flows.
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作者：Fresan, Javier; Jossen, Peter
摘要：We answer in the negative Siegel's question whether all E-functions are polynomial expressions in hypergeometric E-functions. Namely, we show that if an irreducible differential operator of order three annihilates an E-function in the hypergeometric class, then the singularities of its Fourier transform are constrained to satisfy a symmetry property that generically does not hold. The proof relies on Andre ''s theory of E-operators and Katz's computation of the Galois group of hypergeometric d...
