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1.
Rulin Shen Changguo Shao Qinhui Jiang Wujie Shi Victor Mazurov 《Monatshefte für Mathematik》2010,160(3):337-341
Let G be a group and τ e (G) the set of numbers of elements of G of the same order. In this paper, by τ e (G), we give a new characterization of A 5, where A 5 is the alternating group of degree 5. We get the theorem following: Theorem. Let G be a group, ${G\cong A_5}$ if and only if τ e (G) = τ e (A 5) = {1, 15, 20, 24}. 相似文献
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Dedicated to Professor Sh?r? Araki on the occasion of his 60th birthday. 相似文献
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Kalle Kaarli 《Algebra Universalis》2001,45(2-3):345-347
We prove that an equivalence lattice is arithmetical whenever for every and there exists a compatible choice function modulo , having a as a fixed point. The converse holds if L is finite. Received September 30, 1998; accepted in final form December 1, 1998. 相似文献
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Dieter Kratsch 《Discrete Mathematics》2008,308(20):4833-4835
We show that a graph G has no houses and no holes if and only if for every connected induced subgraph H of G and every vertex in H, either the vertex is adjacent to all the other vertices in H, or it forms a 2-pair of H with some other vertex in H. As a consequence, there is a simple linear time algorithm to find a 2-pair in HH-free graphs. We also note that the class of Meyniel graphs admits an analogous characterization. 相似文献
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Hortensia Galeana-Sánchez 《Discrete Mathematics》2012,312(17):2751-2755
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Our main result is the following: Let , , be such that for some arbitrary sequence of positive numbers with . Then .This extends a result from H.-M. Nguyen (2006). To cite this article: J. Bourgain, H.-M. Nguyen, C. R. Acad. Sci. Paris, Ser. I 343 (2006). 相似文献
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John Mighton 《Journal of Combinatorial Theory, Series B》2008,98(6):1253-1258
We give a necessary and sufficient condition for a binary matroid to be graphic. The condition is very natural, but, unlike other similar results, it gives a trivial algorithm for testing graphicness. 相似文献
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We characterize the class of ultraspherical polynomials in between all symmetric orthogonal polynomials on via the special form of the representation of the derivatives by
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Let M n be a compact Willmore submanifold in the unit sphere S n+p . In this note, we investigate the first eigenvalue of the Schrödinger operator L = ?Δ?q on M, where q is some potential function on M, and present a gap estimate for the first eigenvalue of L. 相似文献
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Guiyun Chen 《中国科学A辑(英文版)》1997,40(8):807-812
It is proved that a Suzuki-Ree group can he characterized by the bet of its order components
Project partially supported by the National Natural Science Foundation of China and Ph. D. Foundation of Southwest China Normal
University. 相似文献
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Aner Shalev 《Israel Journal of Mathematics》1994,87(1-3):153-160
LetH, G be finite groups such thatH acts onG and each non-trivial element ofH fixes at mostf elements ofG. It is shown that, ifG is sufficiently large, thenH has the structure of a Frobenius complement. This result depends on the classification of finite simple groups. We conclude
that, ifG is a finite group andA ⊆G is any non-cyclic abelian subgroup, then the order ofG is bounded above in terms of the maximal order of a centralizerC
G(a) for 1≠a ∈A. 相似文献
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A new characterization of Hermite polynomials 总被引:6,自引:0,他引:6
A. K. Varma 《Acta Mathematica Hungarica》1987,49(1-2):169-172
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V. M. Kruglov 《Mathematical Notes》1976,20(6):1049-1051
In this note we show that an infinitely divisible (i.d.) distribution function F is Poisson if and only if it satisfies the conditions F(+0) > 0, for any 0 < ∈ < 1 $$\int_{ - \infty }^{I - E} {\frac{{\left| x \right|}}{{1 + \left| x \right|}}} dF = 0$$ and for any 0 < β < 1 $$\int_0^\infty {e^{\alpha xln(x + 1)} } dF< \infty $$ 相似文献
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Let G be a group and π
e
(G) be the set of element orders of G. Let k ? pe(G){k\in\pi_e(G)} and m
k
be the number of elements of order k in G. Let nse(G) = {mk|k ? pe(G)}{{\rm nse}(G) = \{m_k|k\in\pi_e(G)\}} . In Shen et al. (Monatsh Math, 2009), the authors proved that A4 @ PSL(2, 3), A5 @ PSL(2, 4) @ PSL(2,5){A_4\cong {\rm PSL}(2, 3), A_5\cong \rm{PSL}(2, 4)\cong \rm{PSL}(2,5)} and A6 @ PSL(2,9){A_6\cong \rm{PSL}(2,9)} are uniquely determined by nse(G). In this paper, we prove that if G is a group such that nse(G) = nse(PSL(2, q)), where q ? {7,8,11,13}{q\in\{7,8,11,13\}} , then G @ PSL(2,q){G\cong {PSL}(2,q)} . 相似文献