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共轭类的长和有限群的结构 总被引:4,自引:1,他引:3
设G是有限群,并设Con(G)是由G的一切共轭类组成的集合。本文目的是考察Con(G)的算术结构对G的群结构的影响。我们着重于Con(G)的p-部分结构,并得到关于p-幂零群的两个定理。这里,p表示一个有限群的最小素因子。用这两个定理,我们还得到若干结果,其中两个改进了D.Chillag和M.Herzog关于共轭类长的两个结果。 相似文献
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沿海垦区棉花采用“前期保、中期控、后期催熟”的全生育期化调技术,有利于壮苗、早发,塑造高光效株型,改善蕾铃的营养条件,减少脱落,降低霜后花比例等。棉花每公顷子棉产量较对照增加331.65-424.50公斤,增产幅度9.20-15.40%。 相似文献
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本文将考虑满足所谓SN(p)性质的有限群:对于群阶的某一素因子p,G的共轭类长无平方的p-因子.首先,研究了具有.SN(p)性质的有限群的一般结构描述.然后,给出对任意p∈π满足SN(p)性质的有限群G是π-超可解的若干充分条件(其中π是|G|的某些素因子组成的集合) 相似文献
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设G是有限群,Ns(G)表示G的子群共轭类长构成的集合.本文研究Ns(G)中只有两个元素时有限群G的结构,在非幂零情形时给出了G的完全分类,在幂零情形时获得了G的一些性质. 相似文献
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考察元素的阶如何影响有限群的结构是群论中的一个重要课题.本文研究存在一个正规子群N,N外的元素都是素数阶元的有阶群.主要利用熟知的Thompson的一个定理,获得了这样的有限群. 相似文献
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We determine the structure of all finite groups with four class sizes when two of them are coprime numbers larger than 1. We prove that such groups are solvable and that the set of class sizes is exactly {1, m, n, mk}, where m, n > 1 are coprime numbers and k > 1 is a divisor of n. 相似文献
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《代数通讯》2013,41(9):3503-3516
Abstract Let G be a finite p-solvable group for a fixed prime p. Attach to G a graph Γ p (G) whose vertices are the non-central p-regular conjugacy classes of G and connect two vertices by an edge if their cardinalities have a common prime divisor. In this note we study the structure and arithmetical properties of the p-regular class sizes in p-solvable groups G having Γ p (G) disconnected. 相似文献
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《代数通讯》2013,41(9):4393-4403
Abstract Let Gbe a finite p-solvable group. Let us consider the graph Γ* p (G) whose vertices are the primes which occur as the divisors of the conjugacy classes of p-regular elements of G and two primes are joined by an edge if there exists such a class whose size is divisible by both primes. Suppose that Γ p *(G) is a connected graph, then we prove that the diameter of this graph is at most 3 and this is the best bound. 相似文献
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Let G be a finite group with a non-central Sylow r-subgroup R, Z(G) the center of G, and N a normal subgroup of G. The purpose of this paper is to determine the structure of N under the hypotheses that N contains R and the G-conjugacy class size of every element of N is either i or m. Particularly, it is shown that N is Abelian if N ∩ Z(G)=1 and the G-conjugacy class size of every element of N is either 1 or m. 相似文献
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In the past thirty years, several kinds of quantitative characterizations of finite groups especially finite simple groups have been investigated by many mathematicians. Such as quantitative characterizations by group order and element orders, by element orders alone, by the set of sizes of conjugacy classes, by dimensions of irreducible characters, by the set of orders of maximal abelian subgroups and so on. Here the authors continue this topic in a new area tending to characterize finite simple groups with given orders by some special conjugacy class sizes, such as largest conjugacy class sizes, smallest conjugacy class sizes greater than 1 and so on. 相似文献
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Xianglin Du 《代数通讯》2013,41(4):1345-1359
ABSTRACT Let k(G) be the number of conjugacy classes of finite groups G and π e (G) be the set of the orders of elements in G. Then there exists a non-negative integer k such that k(G) = |π e (G)| + k. We call such groups to be co(k) groups. This article classifies all finite co(1) groups. They are isomorphic to one of the following groups: A 5, L 2(7), S 5, Z 3, Z 4, S 4, A 4, D 10, Hol(Z 5), or Z 3 ? Z 4. 相似文献
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给出了满足下列性质P_4的有限群的分类,对任意4个不同的非中心的共轭类,它们的代表元的阶的公因子为1. 相似文献
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The work is inspired by an article of Herzog, Longobardi, and Maj, who considered groups with a finite number of infinite conjugacy classes. Their main results were obtained under assumption that the FC-center is of finite index in the group. We consider here infinite groups with a finite number of conjugacy classes of any size (FNCC-groups). Hence the FC-center in our case will be finite, but of infinite index in the group. Among results on these groups we give a criterion for a wreath product of FNCC-groups to be an FNCC-group. 相似文献