共查询到20条相似文献,搜索用时 499 毫秒
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A p-group G is called a core- group if for every subgroup H of G (where denotes the normal core of H in G). In this paper, it is proved that the nilpotent class of a finite core-p-group is at most 5 if , which is the best upper bound, and the derived length of a finite core-p-group is at most 3 if , which is also the best upper bound. 相似文献
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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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In this paper we define odd dimensional unitary groups . These groups contain as special cases the odd dimensional general linear groups where R is any ring, the odd dimensional orthogonal and symplectic groups and where R is any commutative ring and further the first author's even dimensional unitary groups where is any form ring. We classify the E-normal subgroups of the groups (i.e. the subgroups which are normalized by the elementary subgroup ), under the condition that R is either a semilocal or quasifinite ring with involution and . Further we investigate the action of by conjugation on the set of all E-normal subgroups. 相似文献
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S.E. Boutiah F. Gregorio A. Rhandi C. Tacelli 《Journal of Differential Equations》2018,264(3):2184-2204
We prove that the realization in , of the elliptic operator with domain generates a strongly continuous analytic semigroup provided that and any constants and . This generalizes the recent results in [4] and in [16]. Moreover we show that is consistent, immediately compact and ultracontractive. 相似文献
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Given a prime number p, a field F with and a positive integer n, we study the class-preserving modifications of Kato–Milne classes of decomposable differential forms. These modifications demonstrate a natural connection between differential forms and p-regular forms. A p-regular form is defined to be a homogeneous polynomial form of degree p for which there is no nonzero point where all the order partial derivatives vanish simultaneously. We define a field to be a field over which every p-regular form of dimension greater than is isotropic. The main results are that for a field F, the symbol length of is bounded from above by and for any , . 相似文献
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Gábor Korchmáros Maria Montanucci Pietro Speziali 《Journal of Pure and Applied Algebra》2018,222(7):1810-1826
Let be the algebraic closure of a finite field of odd characteristic p. For a positive integer m prime to p, let be the transcendence degree 1 function field defined by . Let and . The extension is a non-Galois extension. Let K be the Galois closure of F with respect to H. By Stichtenoth [20], K has genus , p-rank (Hasse–Witt invariant) and a -automorphism group of order at least . In this paper we prove that this subgroup is the full -automorphism group of K; more precisely where Δ is an elementary abelian p-group of order and D has an index 2 cyclic subgroup of order . In particular, , and if K is ordinary (i.e. ) then . On the other hand, if G is a solvable subgroup of the -automorphism group of an ordinary, transcendence degree 1 function field L of genus defined over , then ; see [15]. This shows that K hits this bound up to the constant .Since has several subgroups, the fixed subfield of such a subgroup N may happen to have many automorphisms provided that the normalizer of N in is large enough. This possibility is worked out for subgroups of Δ. 相似文献
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Existence of standing waves of nonlinear Schrödinger equations with potentials vanishing at infinity
Ohsang Kwon 《Journal of Mathematical Analysis and Applications》2012,387(2):920-930
For a singularly perturbed nonlinear elliptic equation , , we prove the existence of bump solutions concentrating around positive critical points of V when nonnegative V is not identically zero for or nonnegative V satisfies for . 相似文献
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Pradeep K. Rai 《Journal of Pure and Applied Algebra》2018,222(2):316-322
Let G be a special p-group minimally generated by elements and having derived subgroup of order . Berkovich asked to find the Schur multiplier and covering groups of such groups G Berkovich and Janko (2011) [1]. We try to give an answer to this question in this article. 相似文献
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In this paper, we consider the following elliptic equation(0.1) where , , is differentiable in and is a given nonnegative Hölder continuous function in . The asymptotic behavior at infinity and structure of separation property of positive radial solutions with different initial data for (0.1) are discussed. Moreover, the existence and separation property of infinitely many positive solutions for Hardy equation and an equation related to Caffarelli–Kohn–Nirenberg inequality are obtained respectively, as special cases. 相似文献
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John R. Britnell Neil Saunders Tony Skyner 《Journal of Pure and Applied Algebra》2017,221(11):2647-2665
A finite group G is exceptional if it has a quotient Q whose minimal faithful permutation degree is greater than that of G. We say that Q is a distinguished quotient.The smallest examples of exceptional p-groups have order . For an odd prime p, we classify all pairs where G has order and Q is a distinguished quotient. (The case has already been treated by Easdown and Praeger.) We establish the striking asymptotic result that as p increases, the proportion of groups of order with at least one exceptional quotient tends to 1/2. 相似文献
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We extend the notion of a partial cohomology group to the case of non-unital A and find interpretations of and in the theory of extensions of semilattices of abelian groups by groups. 相似文献
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Douglas P. Hardin Michael C. Northington Alexander M. Powell 《Applied and Computational Harmonic Analysis》2018,44(2):294-311
A sharp version of the Balian–Low theorem is proven for the generators of finitely generated shift-invariant spaces. If generators are translated along a lattice to form a frame or Riesz basis for a shift-invariant space V, and if V has extra invariance by a suitable finer lattice, then one of the generators must satisfy , namely, . Similar results are proven for frames of translates that are not Riesz bases without the assumption of extra lattice invariance. The best previously existing results in the literature give a notably weaker conclusion using the Sobolev space ; our results provide an absolutely sharp improvement with . Our results are sharp in the sense that cannot be replaced by for any . 相似文献
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Zhiqin Lu 《Linear algebra and its applications》2012,436(7):2531-2535