共查询到20条相似文献,搜索用时 640 毫秒
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Marcel Herzog Patrizia Longobardi Mercede Maj 《Journal of Pure and Applied Algebra》2018,222(7):1628-1642
Denote the sum of element orders in a finite group G by and let denote the cyclic group of order n. Suppose that G is a non-cyclic finite group of order n and q is the least prime divisor of n. We proved that and . The first result is best possible, since for each , k odd, there exists a group G of order n satisfying and the second result implies that if G is of odd order, then . Our results improve the inequality obtained by H. Amiri, S.M. Jafarian Amiri and I.M. Isaacs in 2009, as well as other results obtained by S.M. Jafarian Amiri and M. Amiri in 2014 and by R. Shen, G. Chen and C. Wu in 2015. Furthermore, we obtained some -based sufficient conditions for the solvability of G. 相似文献
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Jianbei An Heiko Dietrich Shih-Chang Huang 《Journal of Pure and Applied Algebra》2018,222(12):4020-4039
We consider the finite exceptional group of Lie type (universal version) with , where and . We classify, up to conjugacy, all maximal-proper 3-local subgroups of G, that is, all 3-local which are maximal with respect to inclusion among all proper subgroups of G which are 3-local. To this end, we also determine, up to conjugacy, all elementary-abelian 3-subgroups containing , all extraspecial subgroups containing , and all cyclic groups of order 9 containing . These classifications are an important first step towards a classification of the 3-radical subgroups of G, which play a crucial role in many open conjectures in modular representation theory. 相似文献
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Let e be a positive integer, p be an odd prime, , and be the finite field of q elements. Let . The graph is a bipartite graph with vertex partitions and , and edges defined as follows: a vertex is adjacent to a vertex if and only if and . If and , the graph contains no cycles of length less than eight and is edge-transitive. Motivated by certain questions in extremal graph theory and finite geometry, people search for examples of graphs containing no cycles of length less than eight and not isomorphic to the graph , even without requiring them to be edge-transitive. So far, no such graphs have been found. It was conjectured that if both f and g are monomials, then no such graphs exist. In this paper we prove the conjecture. 相似文献
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Let G be a graph with n vertices and edges, and let be the Laplacian eigenvalues of G. Let , where . Brouwer conjectured that for . It has been shown in Haemers et al. [7] that the conjecture is true for trees. We give upper bounds for , and in particular, we show that the conjecture is true for unicyclic and bicyclic graphs. 相似文献
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A Steiner 2- trade is a pair of disjoint partial Steiner triple systems, each on the same set of points, such that each pair of points occurs in if and only if it occurs in . A Steiner 2- trade is called d-homogeneous if each point occurs in exactly d blocks of (or ). In this paper we construct minimal d-homogeneous Steiner 2- trades of foundation and volume for sufficiently large values of . (Specifically, if is divisible by 3 and otherwise.) 相似文献
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Let V be an n-dimensional vector space over the finite field consisting of q elements and let be the Grassmann graph formed by k-dimensional subspaces of V, . Denote by the restriction of to the set of all non-degenerate linear codes. We show that for any two codes the distance in coincides with the distance in only in the case when , i.e. if n is sufficiently large then for some pairs of codes the distances in the graphs and are distinct. We describe one class of such pairs. 相似文献
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《Discrete Mathematics》2007,307(11-12):1347-1355
A k-ranking of a graph G is a mapping such that any path with endvertices x and y satisfying and contains a vertex z with . The ranking number of G is the minimum k admitting a k-ranking of G. The on-line ranking number of G is the corresponding on-line invariant; in that case vertices of G are coming one by one so that a partial ranking has to be chosen by considering only the structure of the subgraph of G induced by the present vertices. It is known that . In this paper it is proved that . 相似文献
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《Discrete Mathematics》2007,307(17-18):2235-2245