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1.
Let З be a complete set of Sylow subgroups of a finite group G, that is, З contains exactly one and only one Sylow p-subgroup of G for each prime p. A subgroup of a finite group G is said to be З-permutable if it permutes with every member of З. Recently, using the Classification of Finite Simple Groups, Heliel, Li and Li proved tile following result: If the cyclic subgroups of prime order or order 4 iif p = 2) of every member of З are З-permutable subgroups in G, then G is supersolvable. In this paper, we give an elementary proof of this theorem and generalize it in terms of formation.  相似文献   

2.
A idempotent quasigroup (Q, o) of order n is equivalent to an n(n-1)×3 partial orthogonal array in which all of rows consist of 3 distinct elements. Let X be a (n+1)-set. Denote by T(n+1) the set of (n+1)n(n-1) ordered triples of X with the property that the 3 coordinates of each ordered triple are distinct. An overlarge set of idempotent quasigroups of order n is a partition of T(n+1) into n+1 n(n-1)×3 partial orthogonal arrays A_x, x∈X based on X\{x}. This article gives an almost complete solution of overlarge sets of idempotent quasigroups.  相似文献   

3.
张新政  王勇  班桂宁 《数学季刊》2003,18(4):369-377
In this paper, we determine the order of automorphism group of p-groups in the third family (Φ3 ) and the fourth family (Φ4 ) in [ 1 ], whose order is p^6 ( p ≥ 3). Here p denotes an odd prime.  相似文献   

4.
A RECOGNITION OF SIMPLE GROUPS PSL(3, q) BY THEIR ELEMENT ORDERS   总被引:2,自引:0,他引:2  
For any group G, denote byπe(G) the set of orders of elements in G. Given a finite group G, let h(πe (G)) be the number of isomorphism classes of finite groups with the same set πe(G) of element orders. A group G is called k-recognizable if h(πe(G)) = k <∞, otherwise G is called non-recognizable. Also a 1-recognizable group is called a recognizable (or characterizable) group. In this paper the authors show that the simple groups PSL(3,q), where 3 < q≡±2 (mod 5) and (6, (q-1)/2) = 1, are recognizable.  相似文献   

5.
钱国华 《数学进展》2002,31(1):77-78
Let G be a finite group, Irr(G) denotes the set of irreducible complex characters of G and gGthe conjugacy class of G containing element g. A well-known theorem of Burnside([1,Theorem3. 15]) states that every nonlinear X E Irr(G) has a zero on G, that is, an element x (or a conjugacyclass xG) of G with x(x) = 0. So, if the number of zeros of character table is very small, we mayexpect, the structure of group is heavily restricted. For example, [2, Proposition 2.7] claimesthat G is a Fro…  相似文献   

6.
二次极大子群皆是$PSC^{*}$-群的有限群   总被引:1,自引:0,他引:1       下载免费PDF全文
This paper discusses the influence of minimal subgroups on the structure of finite groups and gives the structures of finite groups all of whose second maximal subgroups are PSC^*-groups.  相似文献   

7.
We consider proper Klein surfaces X of algebraic genus p ≥ 2, having an automorphism φ of prime order n with quotient space X/(φ) of algebraic genus q. These Klein surfaces axe called q-n-gonal surfaces and they are n-sheeted covers of surfaces of algebraic genus q. In this paper we extend the results of the already studied cases n ≤ 3 to this more general situation. Given p ≥ 2, we obtain, for each prime n, the (admissible) values q for which there exists a q-n-gonal surface of algebraic genus p. Furthermore, for each p and for each admissible q, it is possible to check all topological types of q-n-gonal surfaces with algebraic genus p. Several examples are given: q-pentagonal surfaces and q-n-gonal bordered surfaces with topological genus g = 0, 1.  相似文献   

8.
Let H be a subgroup of a finite group G. H is nearly SS-embedded in G if there exists an S-quasinormal subgroup K of G, such that HK is S-quasinormal in G and H ∩ K ≤ HseG, where HseG is the subgroup of H, generated by all those subgroups of H which are S-quasinormally embedded in G. In this paper, the authors investigate the influence of nearly SS-embedded subgroups on the structure of finite groups.  相似文献   

9.
Let ω1 and ω 2 be two homogeneous words and suppose that they respectively define the varieties Vω 1 and Vω2 of groups. Denote by θωi the standard exponent of ωi for i =1, 2, which was introduced in Ref. [1]. We obtain that if Vω1 lohtian Vω2, then ω1θ|θ ω2.  相似文献   

10.
The torsion conjecture says: for any abelian variety A defined over a number field k, the order of the torsion subgroup of A(k) is bounded by a constant C(k,d) which depends only on the number field k and the dimension d of the abelian variety. The torsion conjecture remains open in general. However, in this paper, a short argument shows that the conjecture is true for more general fields if we consider linear groups instead of abelian varieties. If G is a connected linear algebraic group defined over a field k which is finitely generated over Q,Г is a torsion subgroup of G(k). Then the order of Г is bounded by a constant C'(k, d) which depends only on k and the dimension d of G.  相似文献   

11.
On the basis of a random sample of size n on an m-dimensional random vector X, this note proposes a class of estimators fn(p) of f(p), where f is a density of X w.r.t. a σ-finite measure dominated by the Lebesgue measure on Rm, p = (p1,…,pm), pj ≥ 0, fixed integers, and for x = (x1,…,xm) in Rm, f(p)(x) = ?p1+…+pm f(x)/(?p1x1 … ?pmxm). Asymptotic unbiasedness as well as both almost sure and mean square consistencies of fn(p) are examined. Further, a necessary and sufficient condition for uniform asymptotic unbisedness or for uniform mean square consistency of fn(p) is given. Finally, applications of estimators of this note to certain statistical problems are pointed out.  相似文献   

12.
Starting with Euler's theorem that any odd perfect number n has the form n = pepi2eipk2ek, where p, p1,…,pk are distinct odd primes and pe ≡ 1 (mod 4), we show that extensive subsets of these numbers (so described) can be eliminated from consideration. A typical result says: if pe, pi2ei,…,pr2er are all of the prime-power divisors of such an n with ppi ≡ 1 (mod 4), then the ordered set {e1,…,er} contains an even number or odd number of odd numbers according as eporep (mod 8).  相似文献   

13.
In this paper we study the isometric extension problem and show that every surjective isometry between the unit spheres of Lp (μ) (1 p ∞, p≠2) and a Banach space E can be extended to a linear isometry from Lp(μ) onto E, which means that if the unit sphere of E is (metrically) isometric to the unit sphere of Lp(μ), then E is linearly isometric to Lp(μ). We also prove that every surjective 1-Lipschitz or anti-1-Lipschitz map between the unit spheres of Lp (μ1, H1) and Lp(μ2,H2) must be an isometry and can be extended to a linear isometry from Lp (μ1,H1) to Lp (μ2,H2), where H1 and H2 are Hilbert spaces.  相似文献   

14.
The Hardy space Hpis not locally convex if 0 < p < 1, even though its conjugate space(Hp) separates the points of Hp. But then it is locally p-convex, and its conjugate cone(Hp) p is large enough to separate the points of Hp. In this case, the conjugate cone can be used to replace its conjugate space to set up the duality theory in the p-convex analysis. This paper deals with the representation problem of the conjugate cone(Hp) p of Hpfor 0 < p ≤ 1, and obtains the subrepresentation theorem(Hp) p L∞(T, C p).  相似文献   

15.
Let p be an odd prime, let d be a positive integer such that (d,p?1)=1, let r denote the p-adic valuation of d and let m=1+3+32+…+3r. It is shown that for every p-adic integer n the equation Σi=1mXid=n has a nontrivial p-adic solution. It is also shown that for all p-adic units a1, a2, a3, a4 and all p-adic integers n the equation Σi=14aiXip=n has a nontrivial p-adic solution. A corollary to each of these results is that every p-adic integer is a sum of four pth powers of p-adic integers.  相似文献   

16.
We define a new map between codes over Fp + uFp + u2Fp and Fp which is different to that defined in [2]. It is proved that the image of the linear cyclic code over the commutative ring Fp + uFp + u2Fp with length n under this map is a distance-invariant quasi-cyclic code of index p2 with length p2n over Fp. Moreover, it is proved that, if (np) = 1, then every code with length p2n over Fp which is the image of a linear (1 − u2)-cyclic code with length n over Fp + uFp + u2Fp under this map is permutation equivalent to a quasi-cyclic code of index p2.  相似文献   

17.
Let G be a finite group. Let n be a positive integer and p a prime coprime to n. In this paper we prove that if the set of conjugacy class sizes of primary and biprimary elements of group G is {1,p a , p a n}, then GG 0 × H, where H is abelian and G 0 contains a normal subgroup M × P 0 of index p. Moreover, M × P 0 is the set of all elements of G 0 of conjugacy class sizes p a or 1, where M is an abelian π(n)-subgroup of G 0 and P 0 is an abelian p-subgroup of G 0, neither being central in G. Finally, p a = p and P/P 0 acts fixed-point-freely on M and ?(P) ≤ Z(P). This is an extension of Alan Camina’s theorems on the structure of groups whose set of conjugacy class size is {1,p a , p a q b }, where p and q are two distinct primes.  相似文献   

18.
We prove the following theorem:Let T be an order preserving nonexpansive operator on L 1 (μ) (or L 1 + ) of a σ-finite measure, which also decreases theL -norm, and let S=tI+(1?t)T for 0<t<1. Then for everyf ∈ Lp (1<p<∞),the sequence S nf converges weakly in Lp. (The assumptions do not imply thatT is nonexpansive inL p for anyp>1, even ifμ is finite.) For the proof we show that ∥S n+1 f?S nf∥ p → 0 for everyfL p, 1<p<∞, and apply toS the following theorem:Let T be order preserving and nonexpansive in L 1 + , and assume that T decreases theL -norm. Then forgL p (1<p<∞) Tng is weakly almost convergent. If forf ∈ Lp we have T n+1 f?T n f → 0weakly, then T nf converges weakly in Lp (1<p<∞).  相似文献   

19.
This paper is devoted to give the connections between Carleson measures for Besov-Sobolev spaces Bpσ (B) and p-Carleson measure in the unit ball of Cn. As applications, we characterize the Riemann-Stieltjes operators and multipliers acting on Bpσ (B) spaces by means of Carleson measures for Bpσ (B).  相似文献   

20.
It is shown that odd integers k such that k · 2n + 1 is prime for some positive integer n have a positive lower density. More generally, for any primes p1, …, pr, the integers k such that k is relatively prime to each of p1,…, pr, and such that k · p1n1p2n2prnr + 1 is prime for some n1,…, nr, also have a positive lower density.  相似文献   

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