共查询到20条相似文献,搜索用时 15 毫秒
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O. A. Shpyrko 《Moscow University Mathematics Bulletin》2008,63(1):22-26
V.S. Monakhov’s conjecture concerning an estimate of the nilpotent π-length of a π-solvable group G is confirmed in the case l p (G) ≤ 1 for all p ∈ π ? {q} and q ∈ π. New estimates of the nilpotent π-length of a π-solvable group with a supersolvable π-Hall subgroup are also obtained. 相似文献
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O. A. Shpyrko 《Journal of Mathematical Sciences》2013,193(4):631-638
The concept of the derived π-length for finite π-soluble groups is introduced and its elementary properties are described. The dependence between the π-length, nilpotent π-length, and derived π-length, and also between the derived and nilpotent lengths of a π-Hall subgroup, is determined. 相似文献
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Let G be a finite group having a π-subgroup H such that |G: H| is not divisible by the numbers in π. In this case, the subgroup H is referred to as a π-Hall subgroup, and the group G by itself is referred to as a E π -group. If, moreover, the group H is supersolvable, then G is referred to as an E π u -group. It is proved in the paper that the class of all E π u -groups is a solvably saturated formation, and the proof is carried out without using the classification of finite groups. 相似文献
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Norbert Kaiblinger 《Indagationes Mathematicae》2009,20(2):233-246
The Segal-Shale-Weil representation associates to a symplectic transformation of the Heisenberg group an intertwining operator, called metaplectic operator. We develop an explicit construction of metaplectic operators for the Heisenberg group H(G) of a finite abelian group G, an important setting in finite time-frequency analysis. Our approach also yields a simple construction for the multivariate Euclidean case G = ?d. 相似文献
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Let G be a finite group and π be a set of primes. Put ${d_{\pi}(G) = k_{\pi}(G)/|G|_{\pi}}$ , where ${k_{\pi}(G)}$ is the number of conjugacy classes of π-elements in G and |G| π is the π-part of the order of G. In this paper we initiate the study of this invariant by showing that if ${d_{\pi}(G) > 5/8}$ then G possesses an abelian Hall π-subgroup, all Hall π-subgroups of G are conjugate, and every π-subgroup of G lies in some Hall π-subgroup of G. Furthermore, we have ${d_{\pi}(G) = 1}$ or ${d_{\pi}(G) = 2/3}$ . This extends and generalizes a result of W. H. Gustafson. 相似文献
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Weidong Gao 《Journal of Pure and Applied Algebra》2010,214(6):898-909
Let G be a non-cyclic finite solvable group of order n, and let S=(g1,…,gk) be a sequence of k elements (repetition allowed) in G. In this paper we prove that if , then there exist some distinct indices i1,i2,…,in such that the product gi1gi2?gin=1. This result substantially improves the Erd?s-Ginzburg-Ziv theorem and other existing results. 相似文献
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We prove that if G is a finite simple group which is the unit group of a ring, then G is isomorphic to: (a) a cyclic group of order 2; or (b) a cyclic group of prime order 2k−1 for some k; or (c) a projective special linear group PSLn(F2) for some n≥3. Moreover, these groups do all occur as unit groups. We deduce this classification from a more general result, which holds for groups G with no non-trivial normal 2-subgroup. 相似文献
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Let G be a simple algebraic group of type G2 over an algebraically closed field of characteristic 2. We give an example of a finite group Γ with Sylow 2-subgroup Γ2 and an infinite family of pairwise non-conjugate homomorphisms ρ: Γ → G whose restrictions to Γ2 are all conjugate. This answers a question of Burkhard Külshammer from 1995. We also give an action of Γ on a connected unipotent group V such that the map of 1-cohomologies H1(Γ, V) → H1(Γp, V) induced by restriction of 1-cocycles has an infinite fibre. 相似文献
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Siberian Mathematical Journal - Given a nonempty set π of primes, call a nilpotent group π-bounded whenever it has a central series whose every factor F is such that: In every quotient... 相似文献
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A. E. Zalesski 《Archiv der Mathematik》2013,100(3):221-230
The famous Gelfand–Graev character of a group of Lie type G is a multiplicity free character of shape ν G , where ν is a suitable degree 1 character of a Sylow p-subgroup and p is the defining characteristic of G. We show that, for an arbitrary non-abelian simple group G, if ν is a linear character of a Sylow p-subgroup of G such that ν G is multiplicity free, then G is isomorphic to either a group of Lie type in defining characteristic p, or to a group PSL(2, q), where either p = q + 1, or p = 2 and q + 1 or q ? 1 is a 2-power. 相似文献
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Let H, A and B be subgroups of a group G. We call the pair (A, B) a θ-pair for H in G if: (i) áH, A? = G{\langle H, A\rangle=G} and B = (A ∩ H)
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1/B is a proper subgroup of A/B and
A1/B \vartriangleleft G/B{{A_1/B \vartriangleleft G/B}}, then G 1 áH, A1?{G\neq \langle H, A_1\rangle}. In this paper, we study the θ-pairs for 2-maximal subgroups of a group, which imply a group to be solvable or supersolvable. 相似文献
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We describe some methods for constructing Fischer classes of finite groups by means of the operators defined by given properties of Hall π-subgroups. It is in particular proved that, for a Fischer class $\mathfrak{F}$ and a set of primes π, the class of all finite π-soluble $C_\pi \mathfrak{F}$ -groups, i.e., of all groups whose Hall π-subgroups belong to $\mathfrak{F}$ , is a Fischer class. 相似文献
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Stephen Bruce Sontz 《Mathematische Zeitschrift》2011,269(1-2):9-28
We prove identities involving the integral kernels of three versions (two being introduced here) of the Segal?CBargmann transform associated to a finite Coxeter group acting on a finite dimensional, real Euclidean space (the first version essentially having been introduced around the same time by Ben Sa?d and ?rsted and independently by Soltani) and the Dunkl heat kernel, due to R?sler, of the Dunkl Laplacian associated with the same Coxeter group. All but one of our relations are originally due to Hall in the context of standard Segal?CBargmann analysis on Euclidean space. Hall??s results (trivial Dunkl structure and arbitrary finite dimension) as well as our own results in???-deformed quantum mechanics (non-trivial Dunkl structure, dimension one) are particular cases of the results proved here. So we can understand all of these versions of the Segal?CBargmann transform associated to a Coxeter group as Hall type transforms. In particular, we define an analogue of Hall??s Version C generalized Segal?CBargmann transform which is then shown to be Dunkl convolution with the Dunkl heat kernel followed by analytic continuation. In the context of Version C we also introduce a new Segal?CBargmann space and a new transform associated to the Dunkl theory. Also we have what appears to be a new relation in this context between the Segal?CBargmann kernels for Versions A and C. 相似文献