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特征标表中零点个数很少的有限可解群 总被引:2,自引:1,他引:2
(1)与(2)均曾研究过有某特征标恰在两个共轭类上取非零值的有限群。本文讨论上述情形的另一极端,即每个不可约特征标至多在p个共轭类上取零值的有限可解群,这里p为群阶的最小素因子,通过对极小非交换商群的分析,我们将刻划这类群的结构。 相似文献
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设G是个有限可解解,若对G的每个商群H,H的正规Abel子群都是可以由2元生成的,则称G为AD2-群,在本文里,我们证明了:如果G是个AD2-群,那么G是3元生定的,且G^(6)=1。另外,我们举了2个例子,说明这些界都是最好的。 相似文献
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关于允许一个无不动点自同构群的有限群的可解性 总被引:1,自引:0,他引:1
关于允许一个无不动点自同构(群)的有限群的可解性的猜想是有限群研究中的一个重要问题。结果比较丰富的是限制该自同构群为一个p-群的情形。Thompson于1959年证明了p阶群的情形。Martineail于1971年证明了初等Abel p-群的情形。Rickman于1979年证明了p2阶群的情形。本文借助Glauberman的一个定理,对p=2或3的一般情形给出了肯定的回答。实际上是用较初等的方法证明了更为广泛一些的结论。 相似文献
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Kamal Aziziheris 《Algebras and Representation Theory》2013,16(3):747-754
Let cd(G) be the set of all irreducible complex character degrees of a finite group G. In this paper, we show that if a, b, and c are pairwise relatively prime integers and ${\rm{cd}} \left(G\right) \subseteq \{1, a, b, c, ab, ac\}$ , then either G is solvable or {a, b, c}?=?{2 f ???1, 2 f , 2 f ?+?1} for some $f \geqslant 2$ and cd (G)?=?{1, a, b, c}. 相似文献
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Gerson Petronilho 《Journal of Differential Equations》2002,184(1):48-61
We consider a class of sum of squares operators on a torus and we prove that global solvability is equivalent to an algebraic condition involving simultaneously approximable vectors. 相似文献
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H is called an ? p -embedded subgroup of G, if there exists a p-nilpotent subgroup B of G such that H p ∈ Syl p (B) and B is ? p -supplemented in G. In this paper, by considering prime divisor 3, 5, or 7, we use ? p -embedded property of primary subgroups to investigate the solvability of finite groups. The main result is follows. Let E be a normal subgroup of G, and let P be a Sylow 5-subgroup of E. Suppose that 1 < d ? |P| and d divides |P|. If every subgroup H of P with |H| = d is ?5-embedded in G, then every composition factor of E satisfies one of the following conditions: (1) I/C is cyclic of order 5, (2) I/C is 5′-group, (3) I/C ? A5. 相似文献
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A. Kh. Amirov 《Siberian Mathematical Journal》1987,28(6):865-872
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D. A. Nomirovskii 《Ukrainian Mathematical Journal》2005,57(3):440-452
We consider the problem of solvability and optimization for a pseudohyperbolic operator of the general form. We prove theorems
on existence and uniqueness for various right-hand sides of the equation. The results obtained are applied to the problem
of trajectory-final controllability.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 3, pp. 366–376, March, 2005. 相似文献
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Andrey Amosov Grigory Panasenko 《Nonlinear Analysis: Theory, Methods & Applications》2010,72(11):3953-3968
We consider the integro-differential Burgers equation which appears in nonlinear acoustics. The integral term in the right-hand side describes the relaxation (memory) effects. The global existence and uniqueness of solution is proved. The smoothness of the solution is studied.In the case when the coefficients of the equation rapidly oscillate, we replace it by the homogenized equation with constant coefficients and prove the error estimates. 相似文献
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David Pokrass 《代数通讯》2013,41(3):225-239