共查询到20条相似文献,搜索用时 140 毫秒
1.
主要探讨了秩大于或者等于p-1的可除阿贝尔p-群的p-自同构群,并且得到这些p-自同构如何作用在该可除阿贝尔p-群上.这些结论有助于进一步理解 ?ernikov p-群的结构. 相似文献
2.
Mark L. Lewis 《代数通讯》2013,41(5):1994-2002
In this article, we show that if p is a prime and G is a p-solvable group, then |G: O p (G)| p ≤ (b(G) p /p)1/(p?1), where b(G) is the largest character degree of G. If p is an odd prime that is not a Mersenne prime or if the nilpotence class of a Sylow p-subgroup of G is at most p, then |G: O p (G)| p ≤ b(G). 相似文献
3.
Claude Marion 《代数通讯》2013,41(3):853-925
Let p 1, p 2, p 3 be primes. This is the second article in a series of three on the (p 1, p 2, p 3)-generation of the finite projective special unitary and linear groups PSU3(p n ), PSL3(p n ), where we say a noncyclic group is (p 1, p 2, p 3)-generated if it is a homomorphic image of the triangle group T p 1, p 2, p 3 . This paper is concerned with the case where p 1 = 2 and p 2 = p 3. We determine for any prime p 2 the prime powers p n such that PSU3(p n ) (respectively, PSL3(p n )) is a quotient of T = T 2, p 2, p 2 . We also derive the limit of the probability that a randomly chosen homomorphism in Hom(T, PSU3(p n )) (respectively, Hom(T, PSL3(p n ))) is surjective as p n tends to infinity. 相似文献
4.
M. Z. Garaev 《Monatshefte für Mathematik》2006,160(1):127-138
We obtain nontrivial estimates of character sums over short intervals for almost all moduli. These bounds and the method of
Karatsuba for solving multiplicative ternary problems are used to prove that for π(X)(1 + o(1)) primes p,p ≤ X, there are p(1 + o(1)) residue classes modulo p of the form xy (mod p), where 1 ≤ x, y ≤ p?(log p)1,087. We also prove that for any prime p there are p(1 + o(1)) residue classes modulo p of the form xy* (mod p), where 1 ≤ x, y ≤ p?(log p)1+o(1) and y* is defined by yy* ≡ 1 (mod p). 相似文献
5.
Yakov Berkovich 《Israel Journal of Mathematics》2010,180(1):371-412
Let G be a finite p-group. If p = 2, then a nonabelian group G = Ω1(G) is generated by dihedral subgroups of order 8. If p > 2 and a nonabelian group G = Ω1(G) has no subgroup isomorphic to Sp2{\Sigma _{{p^2}}}, a Sylow p-subgroup of the symmetric group of degree p
2, then it is generated by nonabelian subgroups of order p
3 and exponent p. If p > 2 and the irregular p-group G has < p nonabelian subgroups of order p
p
and exponent p, then G is of maximal class and order p
p+1. We also study in some detail the p-groups, containing exactly p nonabelian subgroups of order p
p
and exponent p. In conclusion, we prove three new counting theorems on the number of subgroups of maximal class of certain type in a p-group. In particular, we prove that if p > 2, and G is a p-group of order > p
p+1, then the number of subgroups ≅ ΣSp2{\Sigma _{{p^2}}} in G is a multiple of p. 相似文献
6.
Ken-iti Sato 《Annals of the Institute of Statistical Mathematics》1987,39(1):407-415
Summary For a unimodal distribution relations of its modea with its absolute momentβ
p
and central absolute momentγ
p
of orderp are considered. The best constantA
p
andB
p
are given for the inequalities |a|≦A
p
β
p
1/p
(p>0) and |a−m|≦B
p
γ
p
1/p
(p≧1) wherem is the mean. the results follow from discussion of more general moments. 相似文献
7.
M. Z. Garaev 《Monatshefte für Mathematik》2006,148(2):127-138
We obtain nontrivial estimates of character sums over short intervals for almost all moduli. These bounds and the method of
Karatsuba for solving multiplicative ternary problems are used to prove that for π(X)(1 + o(1)) primes p,p ≤ X, there are p(1 + o(1)) residue classes modulo p of the form xy (mod p), where 1 ≤ x, y ≤ p?(log p)1,087. We also prove that for any prime p there are p(1 + o(1)) residue classes modulo p of the form xy* (mod p), where 1 ≤ x, y ≤ p?(log p)1+o(1) and y* is defined by yy* ≡ 1 (mod p). 相似文献
8.
A finite group G is called p
i
-central of height k if every element of order p
i
of G is contained in the k
th
-term ζ
k
(G) of the ascending central series of G. If p is odd, such a group has to be p-nilpotent (Thm. A). Finite p-central p-groups of height p − 2 can be seen as the dual analogue of finite potent p-groups, i.e., for such a finite p-group P the group P/Ω1(P) is also p-central of height p − 2 (Thm. B). In such a group P, the index of P
p
is less than or equal to the order of the subgroup Ω1(P) (Thm. C). If the Sylow p-subgroup P of a finite group G is p-central of height p − 1, p odd, and N
G
(P) is p-nilpotent, then G is also p-nilpotent (Thm. D). Moreover, if G is a p-soluble finite group, p odd, and P ∈ Syl
p
(G) is p-central of height p − 2, then N
G
(P) controls p-fusion in G (Thm. E). It is well-known that the last two properties hold for Swan groups (see [11]). 相似文献
9.
Ralf Kemper 《Applied Categorical Structures》1999,7(3):279-295
We introduce the categories Vec
p
of p-normed vector spaces, Ban
p
of
p
-Banach spaces, AC
p
of
p
-absolutely and TC
p
of
p
-totally convex spaces (0 < p 1). It will be shown that TC
p
(AC
p
) is the Eilenberg–Moore category of Ban
p
(Vec
p
). Then congruence relations on TC
p
(AC
p
)-spaces are studied. There are many differences between TC
p
(AC
p
)-spaces and totally (absolutely) convex spaces (i.e. p = 1) (Pumplün and Röhrl, 1984, 1985), which will become apparent in Section 4. 相似文献
10.
Tao Feng 《Journal of Algebraic Combinatorics》2009,29(1):91-106
Let p be an odd prime. We first get some non-existence and structural results on (pn,p,pn,n) relative difference sets with gcd(p,n)=1 through a group ring approach. We then give a construction of (p(p+1),p,p(p+1),p+1) relative difference sets with p a Mersenne prime.
Supported by National Natural Science Foundation of China (10331030). 相似文献
11.
Lu Qikeng 《数学学报(英文版)》1998,14(1):1-8
In the complexn-dimensional projective spaceCP
n
, let λ
p
(=4p(p+n)) be the eigen value of the Laplace-Beltrami operator andH
p
be the space of all eigen functions of eigen value λ
p
. The reproducing kernelh
p
(z, w) ofH
p
is constructed explicitly in this paper, and a system of complete orthogohal functions ofH
p
is constructed fromh
p
(z,w)(p=1,2, …).
Partially supported by NSF of China 相似文献
12.
Cp 总被引:1,自引:0,他引:1
Charles A. McCarthy 《Israel Journal of Mathematics》1967,5(4):249-271
The spacec
p is the class of operators on a Hilbert space for which thec
p norm |T|
p
=[trace(T*T)
p/2]1/p
is finite. We prove many of the known results concerningc
p in an elementary fashion, together with the result (new for 1<p<2) thatc
p is as uniformly convex a Banach space asl
p. In spite of the remarkable parallel of norm inequalities in the spacesc
p andl
p, we show thatp ≠ 2, noc
p built on an infinite dimensional Hilbert space is equivalent to any subspace of anyl
p orL
p space.
The author was supported by National Science Foundation Grant GP-5707. 相似文献
13.
Dean Crnković 《Designs, Codes and Cryptography》2006,39(2):247-251
Let p and 2p−1 be prime powers and p ≡ 3 (mod 4). Then there exists a symmetric design with parameters (4p2, 2p2 − p, p2 − p). Thus there exists a regular Hadamard matrix of order 4p2. 相似文献
14.
BaoShanWANG JiPingZHANG 《数学学报(英文版)》2003,19(1):29-34
In this paper,we shall mainly study the p-solvable finite group in terms of p-local rank,and a group theoretic characterization will be given of finite p-solvabel groups with p-local rank two.Theorem A Let G be a finite p-solvable group with p-local rank plr(G)=2 and Op(G)=1.If P is a Sylow p-subgrounp of G,then P has a normal subgroup Q such that P/Q is cyclic or a generalized quaternion 2-group and the p-rank of Q is at most two.Theorem B Let G be a finite p-solvable group with Op(G)=1.Then the p-length lp(G)≤plr(G);if in addition plr(G)=lp (G) and p≥5 is odd,then plr(G)=0 or 1. 相似文献
15.
A survey of orthogonal arrays of strength two 总被引:1,自引:0,他引:1
ASURVEYOFORTHOGONALARRAYSOFSTRENGTHTWOLIUZHANGWEN(刘璋温)(InstituteofAppliedMathematics.theChineseAcademyofScietices.Beijing1000... 相似文献
16.
Paul F. X. Müller 《Israel Journal of Mathematics》1988,63(2):212-222
LetX
D
p
be the span of the Haar function {h
j: J ε D} inL
p (1 <p < ∞) endowed withL
p norm. Then for any finite setD, the spacesX
D
p
andl
*D
p
areK
p-isomorphic whereK
p depends onp only. 相似文献
17.
Haskell P. Rosenthal 《Israel Journal of Mathematics》1970,8(3):273-303
Let 2<p<∞. The Banach space spanned by a sequence of independent random variables inL
p
, each of mean zero, is shown to be isomorphic tol
2,l
p
,l
2⊕l
p
, or a new spaceX
p
, and the linear topological properties ofX
p
are investigated. It is proved thatX
p
is isomorphic to a complemented subspace ofL
p
and another uncomplemented subspace ofL
p
, whence there exists an uncomplemented subspace ofl
p
isomorphic tol
p
. It is also proved thatX
p
is not isomorphic to the previously knownℒ
p
spaces.
The work for this research was partially supported by the National Science Foundation GP-12997. 相似文献
18.
Prime chains are sequences $p_{1}, \ldots , p_{k}Prime chains are sequences p1, ?, pkp_{1}, \ldots , p_{k} of primes for which pj+1 o 1{p_{j+1} \equiv 1} (mod p
j
) for each j. We introduce three new methods for counting long prime chains. The first is used to show that N(x; p) = Oe(x1+e){N(x; p) = O_{\varepsilon}(x^{1+\varepsilon})}, where N(x; p) is the number of chains with p
1 = p and pk £ px{p_k \leq p_x}. The second method is used to show that the number of prime chains ending at p is ≍ log p for most p. The third method produces the first nontrivial upper bounds on H(p), the length of the longest chain with p
k
= p, valid for almost all p. As a consequence, we also settle a conjecture of Erdős, Granville, Pomerance and Spiro from 1990. A probabilistic model
of H(p), based on the theory of branching random walks, is introduced and analyzed. The model suggests that for most p £ x{p \leq x}, H(p) stays very close to e log log x. 相似文献
19.
In this paper, we characterize periodic solutions of p-periodic difference equations. We classify the periods into multiples of p and nonmultiples of p. We show that the elements of the set of multiples of p follow the well-known Sharkovsky’s ordering multiplied by p. On the other hand, we show that the elements of the set Γp of nonmultiples of p are independent in their existence. Moreover, we show the existence of a p-periodic difference equation with infinite Γp-set in which the maps are defined on a compact domain and agree exactly on a countable set. Based on the proposed classification, we give a refinement of Sharkovsky’s theorem for periodic difference equations. 相似文献
20.
Let p be a prime number, p > 2. A closed Riemann surface which can be realized as a p-sheeted covering of the Riemann sphere is called p-gonal, and such a covering is called a p-gonal morphism. If the p-gonal morphism is a cyclic regular covering, the Riemann surface is called a cyclic p-gonal Riemann surface. Accola showed that if the genus is greater than (p − 1)2 the p-gonal morphism is unique. Using the characterization of p-gonality by means of Fuchsian groups we show that there exists a uniparametric family of cyclic p-gonal Riemann surfaces of genus (p − 1)2 which admit two p-gonal morphisms. In this work we show that these uniparametric families are connected spaces and that each of them is the
Riemann sphere without three points. We study the Hurwitz space of pairs (X, f), where X is a Riemann surface in one of the above families and f is a p-gonal morphism, and we obtain that each of these Hurwitz spaces is a Riemann sphere without four points. 相似文献