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We determine the composition factors of the finite groups in which the normalizers of Sylow 3-subgroups are of odd or primary index. 相似文献
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In this paper we have completely determined: (1) all almost simple groups which act 2-transitively on one of their sets of
Sylow p-subgroups. (2) all non-abelian simple groups T whose automorphism group acts 2-transitively on one of the sets of Sylow p-subgroups of T. (3) all finite groups which are 2-transitive on all their sets of Sylow subgroups.
The first author acknowledges the support of OPR Scholarship of Australia
The second author is supported by the National Natural Science Foundation of China. Thanks are also due to the Department
of Mathematics, the University of Western Australia, where he did his part of this work for its hospitality 相似文献
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本文研究了一类单群的数量刻画问题.运用有限单群分类定理及群的元素阶的素图表示的结构定理,获得了有限群G同构于有限正交单群PΩ2n+1(q)(n≥13),当且仅当群的元素的阶的集合一致和群的Sylow子群的正规化子的阶之集合一致.在某种意义推进施武杰教授的一个猜想. 相似文献
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WANG BaoShan & ZHANG ZhiKai LMIB School of Mathematics System Sciences Beihang University Beijing China LMAM School of Mathematical Sciences Peking University Beijing 《中国科学 数学(英文版)》2011,(2)
As a continuation of previous work, in this paper, we mainly study the finite simple groups which have abelian Sylow subgroups in term of p-local rank, especially a group theoretic characterization will be given. 相似文献
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S. G. Kolesnikov 《Algebra and Logic》2005,44(1):25-30
It is proved that values of all complex characters for a Sylow 2-subgroup P of any Weyl group are rational, and every element of P is a product of two involutions in P. Similar results hold also for Sylow 2-subgroups of alternating groups.Supported by RFBR grant No. 03-01-00905.Translated from Algebra i Logika, Vol. 44, No. 1, pp. 44–53, January–February, 2005. 相似文献
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Hiroki Sasaki 《Algebras and Representation Theory》2003,6(4):369-392
We calculate the mod7 cohomology algebra of the Held simple group, whose Sylow 7-subgroups are extraspecial of order 73 and exponent 7. Our method depends on the analysis of the Carlson module of a regular class belonging to a system of parameters. 相似文献
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Groups with complemented subgroups, which are also called completely factorizable groups, were studied by P. Hall, S. N. Chernikov, and N. V. Chernikova (Baeva). For complete factorizability, it is sufficient (Theorem 1) that each proper subgroup have a normal complement in some larger subgroup. A group is said to be weakly factorizable if each of its proper subgroups is complemented in some larger subgroup; the problem of describing finite groups with this property is posed (Question 8.31) in the Kourovka Notebook. Some properties of these groups are considered. The question is studied for Sylow p-subgroups of Chevalley-type groups of characteristic p. The main theorem, Theorem 2, establishes the weak factorizability of the Sylow p-subgroups in the symmetric and alternative groups and in the classical linear groups over fields of characteristic p> 0, excluding the unitary groups of odd dimension > p. 相似文献
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在其Sylow子群上作用双传递的有限群 总被引:2,自引:0,他引:2
本文完全确定了下述类型的有限群:(1)对于某个素数p,在其Sylowp-子群的集合上作用双传递的所有几乎单群;(2)所有的非交换单群T,其自同构群在T的某个Sylowp-子群的集合上作用双传递;(3)在其所有的Sylow子群上双传递的全部有限群. 相似文献
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In the paper, on the basis of the notion of saturation introduced in [1], we give a characterization of locally finite simple groups
with an Abelian Sylow 2-subgroup in the classes of mixed and periodic groups. A part of the main results was announced in [2]. Theorem 2 of the paper generalizes results of [3, 4]. 相似文献
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It is proved that finite simple groups L4(2m), m ⩾ 2, and U4(2m), m ⩾ 2, are, up to isomorphism, recognized by spectra, i.e., sets of their element orders, in the class of finite groups.
As a consequence the question on recognizability by spectrum is settled for all finite simple groups without elements of order
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Supported by RFBR (grant Nos. 05-01-00797 and 06-01-39001), by SB RAS (Complex Integration project No. 1.2), and by the Ministry
of Education of China (Project for Retaining Foreign Expert).
Supported by NSF of Chongqing (CSTC: 2005BB8096).
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Translated from Algebra i Logika, Vol. 47, No. 1, pp. 83–93, January–February, 2008. 相似文献
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Mazur猜想:具有阿贝尔Sylow 2-子群的有限群有正规化子性质.设G是一个有限群,N是G的一个正规子群且Z(G/N)仅有平凡单位,本文建立了由Z(G/N)中单位诱导的G的自同构与N的Coleman自同构之间的联系,在此基础上证明了若G是一个具有阿贝尔Sylow 2-子群的有限群且Z(G/F*(G))仅有平凡单位,则Mazur猜想对G成立. 相似文献
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Gabriel Navarro Benjamin Sambale Pham Huu Tiep 《Journal of Pure and Applied Algebra》2018,222(11):3721-3732
We give two ways to distinguish from the character table of a finite group G if a Sylow 2-subgroup of G has maximal class. We also characterize finite groups with Sylow 3-subgroups of order 3 in terms of their principal 3-block. 相似文献
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Ariel Ish-Shalom 《Israel Journal of Mathematics》1974,18(3):235-242
LetG be a finite group. We say thatG satisfiesI(k) if anyk+1 distinct Sylow 2-subgroups ofG interesect trivially. In this paper we classify all finite groups satisfyingI (3), and all finite simple groups satisfyingI (5). 相似文献
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In the modular representation theory of finite groups the theory of projectivity relative to subgroups is of fundamental importance. To generalize this notion the theory of projectivity relative to modules was introduced by the first author. Our aim is to show some aspects of cohomology theory of finite groups concerning projectivity of modules relative to both subgroups and modules. We shall give some applications to the cohomology theory; especially we shall calculate the mod 2 cohomology algebras of finite groups with wreathed Sylow 2-subgroups. 相似文献
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Julian Brough 《代数通讯》2013,41(12):5347-5361
Let p be a prime. We prove that if a finite group G has non-abelian Sylow p-subgroups, and the class size of every p-element in G is coprime to p, then G contains a simple group as a subquotient which exhibits the same property. In addition, we provide a list of all the simple groups and primes such that the Sylow p-subgroups are non-abelian and all p-elements have class size coprime to p. 相似文献
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John Maginnis 《代数通讯》2013,41(8):2884-2905
The third Conway group Co 3 is one of the 26 sporadic finite simple groups. The cohomology of its Sylow 2-subgroup S is computed, an important step in calculating the mod 2 cohomology of Co 3. The spectral sequence for the central extension of S is described; it collapses at the sixth page. Generators are described in terms of the Evens norm or transfers from subgroups. The central quotient S′ = S/2 is the Sylow 2-subgroup of the symplectic group Sp 6(𝔽2) of six-by-six matrices over the field of two elements. The cohomology of S′ is computed and is detected by restriction to elementary abelian 2-subgroups. 相似文献