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1.
Let L =△ + V be a SchrSdinger operator in Rd, d ≥ 3, where the nonnegative potential V belongs to the reverse HSlder class Sd. We establish the BMOL-boundedness of Riesz transforms З/ЗxiL-1/2, and give the Fefferman-Stein type decomposition of BMOL functions. 相似文献
2.
P. Shumyatsky’s question 11.126 in the “Kourovka Notebook” is answered in the affirmative: it is proved that there exist a
constant c and a function of a positive integer argument f(m) such that if a finite group G admits an automorphism ϕ of order
4 having exactly m fixed points, then G has a normal series G ⩾ H ⩽ N such that |G/H| ⩽ f(m), the quotient group H/N is nilpotent
of class ⩽ 2, and the subgroup N is nilpotent of class ⩽ c (Thm. 1). As a corollary we show that if a locally finite group
G contains an element of order 4 with finite centralizer of order m, then G has the same kind of a series as in Theorem 1.
Theorem 1 generalizes Kovács’ theorem on locally finite groups with a regular automorphism of order 4, whereby such groups
are center-by-metabelian. Earlier, the first author proved that a finite 2-group with an almost regular automorphism of order
4 is almost center-by-metabelian. The proof of Theorem 1 is based on the authors’ previous works dealing in Lie rings with
an almost regular automorphism of order 4. Reduction to nilpotent groups is carried out by using Hall-Higman type theorems.
The proof also uses Theorem 2, which is of independent interest, stating that if a finite group S contains a nilpotent subgroup
T of class c and index |S: T | = n, then S contains also a characteristic nilpotent subgroup of class ⩽ c whose index is bounded
in terms of n and c. Previously, such an assertion has been known for Abelian subgroups, that is, for c = 1.
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Translated from Algebra i Logika, Vol. 45, No. 5, pp. 575–602, September–October, 2006. 相似文献
3.
The aim of this article is to give a generalization of the concept of commutativity degree of a finite group G (denoted by d(G)), to the concept of relative commutativity degree of a subgroup H of a group G (denoted by d(H, G)). We shall state some results concerning the new concept which are mostly new or improvements of known results given in Gustafson (1973) and Moghaddam et al. (2005). Moreover, we shall define the relative nth nilpotency degree of a subgroup of a group and give some results concerning this at the end of the article. 相似文献
4.
Let G be a p ‐group of maximal class of order pm , p ≠ 2, and c (G) the degree of commutativity of G. Let c0 be the nonnegative residue of c modulo p – 1. In this paper, by using only Lie algebra techniques, we prove that 2c ≥ m – 2p + c 0 + 1. Also, we give examples of Lie algebras satisfying the following equalities: In addition, there exist examples of p ‐groups of maximal class satisfying 2c = m – 2p + c0 + 3 for each c0 ∈ [2, p – 2] (see [6, Theorem 4.5]). (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
With the help of continued fractions, we plan to list all the elements of the set Q△ = {aX2 + bXY + cY2 : a,b, c ∈Z, b2 - 4ac = △ with 0 ≤ b 〈 √△}of quasi-reduced quadratic forms of fundamental discriminant △. As a matter of fact, we show that for each reduced quadratic form f = aX2 + bXY + cY2 = (a, b, c) of discriminant △〉0(and of sign σ(f) equal to the sign of a), the quadratic forms associated with f and defined by {〈a+bu+cu2,b+2cu.c〉},with 1≤σ(f)u≤b/2|c| (whenever they exist), 〈c,-b-2cu,a+bu+cu2〉 with b/2|c|≤σ(f)u≤[w(f)]=[b+√△/2|c|], are all different from one another and build a set I(f) whose cardinality is #I(f)={1+[ω(f)],when(2c)|b,[ω(f)],when (2c)|b. If f and g are two different reduced quadratic forms, we show that I(f) ∩ I(g) = Ф. Our main result is that the set Q△ is given by the disjoint union of all I(f) with f running through the set of reduced quadratic forms of discriminant △〉0. This allows us to deduce a formula for #(Q△) involving sums of partial quotients of certain continued fractions. 相似文献
6.
A. Jaikin-Zapirain 《Proceedings of the American Mathematical Society》2005,133(10):2817-2820
In this work we solve a conjecture of Y. Barnea and M. Isaacs about centralizer sizes and the nilpotency class in nilpotent finite-dimensional Lie algebras and finite -groups.
7.
Zhengxing Li & Jinke Hai 《数学研究通讯:英文版》2011,27(3):227-233
Let $G$ be a finite group, $H ≤ G$ and $R$ be a commutative ring with
an identity $1_R$. Let $C_{RG}(H) = \{ α ∈ RG|αh= hα$ for all $h ∈ H \}$, which is called
the centralizer subalgebra of $H$ in $RG$. Obviously, if $H = G$ then $C_{RG}(H)$ is just
the central subalgebra $Z(RG)$ of $RG$. In this note, we show that the set of all $H$-conjugacy class sums of $G$ forms an $R$-basis of $C_{RG}(H)$. Furthermore, let $N$ be a
normal subgroup of $G$ and $γ$ the natural epimorphism from $G$ to $\overline{G}= G/N$. Then $γ$ induces an epimorphism from $RG$ to $R\overline{G}$, also denoted by $γ$. We also show that if $R$ is a field of characteristic zero, then $γ$ induces an epimorphism from $C_{RG}(H)$ to $C_{R\overline{G}}(\overline{H})$, that is, $γ(C_{RG}(H)) = C_{R\overline{G}}(\overline{H})$. 相似文献
8.
Jiangtao Shi 《代数通讯》2013,41(10):3916-3922
As an important application of Thompson's theorem [9, Theorem 10.4.2], a finite group is solvable if it has an abelian maximal subgroup. In this article, we mainly investigate the influence of some quantitative properties of abelian subgroups on solvability of finite groups. Some new results are obtained. 相似文献
9.
The Monster group M contains a pair {C,N} of subgroups, where is the centralizer of an involution and N22+11+211.(M24×Sym3) is the normalizer of an elementary subgroup of order four with N∩C having index three in N. The amalgam {C,N} plays an important role in the existing constructions and uniqueness proofs for the Monster. We suggest a transparent construction of this amalgam. 相似文献
10.
Peter Schmid 《Archiv der Mathematik》2017,108(2):113-121
For any prime p and positive integers c, d there is up to isomorphism a unique p-group \({G_{d}^{c}(p)}\) of least order having any (finite) p-group G with rank \({d(G) \le d}\) and Frattini class \({c_{p}(G) \le c}\) as epimorphic image. Here \({c_{p}(G) = n}\) is the least positive integer such that G has a central series of length n with all factors being elementary. This “disposition” p-group \({G_{d}^{c}(p)}\) has been examined quite intensively in the literature, sometimes controversially. The objective of this paper is to present a summary of the known facts, and to add some new results. For instance we show that for \({G = G_{d}^{c}(p)}\) the centralizer \({C_{G}(x) = \langle Z(G), x \rangle}\) whenever \({x \in G}\) is outside the Frattini subgroup, and that for odd p and \({d \ge 2}\) the group \({E = G_{d}^{c+1}(p)/(G_{d}^{c+1}(p))^{p^{c}}}\) is a distinguished Schur cover of G with \({E/Z(E) \cong G}\). We also have a fibre product construction of \({G_{d}^{c+1}(p)}\) in terms of \({G = G_{d}^{c}(p)}\) which might be of interest for Galois theory. 相似文献
11.
Let G be a finite group and δ(G) denote the number of conjugacy classes of all non-cyclic subgroups of G. The symbol π(G) denotes the set of the prime divisors of |G|. In [7], Meng and Li showed the inequality δ(G)≥2|π(G)|?2, where G is non-cyclic solvable group. In this paper, we describe the finite groups G such that δ(G) = 2|π(G)|?2. Another aim of this paper would show δ(G)≥M(G)+2 for unsolvable groups G and the equality holds ?G?A5 or SL(2,5), where M(G) denotes the number of conjugacy classes of all maximal subgroups of G. 相似文献
12.
Alexei Kanel-Belov Sergey Grigoriev Andrey Elishev Jie-Tai Yu Wenchao Zhang 《代数通讯》2018,46(9):3926-3938
We study the problem of lifting of polynomial symplectomorphisms in characteristic zero to automorphisms of the Weyl algebra by means of approximation by tame automorphisms. In 1983, Anick proved the fundamental result on approximation of polynomial automorphisms. We obtain similar approximation theorems for symplectomorphisms and Weyl algebra authomorphisms. We then formulate the lifting problem. More precisely, we prove the possibility of lifting of a symplectomorphism to an automorphism of the power series completion of the Weyl algebra of the corresponding rank. The lifting problem has its origins in the context of deformation quantization of the a?ne space and is closely related to several major open problems in algebraic geometry and ring theory.This paper is a continuation of the study [19]. 相似文献
13.
Cheng and Tang [Biometrika, 88 (2001), pp. 1169–1174] derived an upper bound on the maximum number of columns that can be accommodated in a two‐symbol supersaturated design (SSD) for a given number of rows () and a maximum in absolute value correlation between any two columns (). In particular, they proved that for (mod ) and . However, the only known SSD satisfying this upper bound is when . By utilizing a computer search, we prove that for , and . These results are obtained by proving the nonexistence of certain resolvable incomplete blocks designs. The combinatorial properties of the RIBDs are used to reduce the search space. Our results improve the lower bound for SSDs with rows and columns, for , and . Finally, we show that a skew‐type Hadamard matrix of order can be used to construct an SSD with rows and columns that proves . Hence, we establish for and for all (mod ) such that . Our result also implies that when is a prime power and (mod ). We conjecture that for all and (mod ), where is the maximum number of equiangular lines in with pairwise angle . 相似文献
14.
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16.
17.
Álvaro Muñoz 《代数通讯》2018,46(9):3873-3888
In this paper we give a complete classification of pointed fusion categories over ? of global dimension 8. We first classify the equivalence classes of pointed fusion categories of dimension 8, and then we proceed to determine which of these equivalence classes have equivalent categories of modules following the procedure presented in [9, 11]. The results of this paper permit to recover the classification of twisted quantum doubles of groups of order 8 up to gauge equivalence of braided quasi-Hopf algebras that was previously done in [6] and [5]. 相似文献
18.
Ladislav Bican 《代数通讯》2013,41(11):4098-4103
It is well-known (see [13]) that a hereditary torsion theory τ for the category R-mod is noetherian if and only if the class of all τ-torsionfree τ-injective modules is closed under arbitrary direct sums. So, it is natural to investigate the hereditary torsion theories having the property that the class of all τ-torsionfree injective modules is closed under arbitrary direct sums, which are called ?-noetherian. These torsion theories have been studied by Teply in [16]. In the second part of this note we shall study the weakly exact hereditary torsion theories, which generalize the exact one's. 相似文献
19.
20.
Haicheng Zhang 《代数通讯》2018,46(6):2551-2560
In this note, let 𝒜 be a finitary hereditary abelian category with enough projectives. By using the associativity formula of Hall algebras, we give a new proof of the main theorem in [17], which states that the Bridgeland Hall algebra of 2-cyclic complexes of projective objects in 𝒜 is isomorphic to the Drinfeld double Hall algebra of 𝒜. 相似文献