共查询到20条相似文献,搜索用时 109 毫秒
1.
W. Mack Hill 《Israel Journal of Mathematics》1974,19(3):208-211
A nonabelianp-group with cyclic center cannot occur as a normal subgroup contained in the Frattini subgroup of ap-closed group. If a nonabelian normal subgroup of orderp
n
and nilpotence classk is contained in the Frattini subgroup of ap-closed group, then its exponent is a divisor ofp
n−k
. This fact is used to derive a relation among the order, number of generators, exponent, and class of the Frattini subgroup,
forp-groups. Finally, it is conjectured that a nonabelianp-group having center of orderp cannot occur as a normal subgroup contained in the Frattini subgroup of any finite group. A proof is given forp-supersolvable groups. 相似文献
2.
Yakov Berkovich 《Israel Journal of Mathematics》2013,194(2):831-869
We study the subgroup structure of some two-generator p-groups and apply the obtained results to metacyclic p-groups. For metacyclic p-groups G, p > 2, we do the following: (a) compute the number of nonabelian subgroups with given derived subgroup, show that (ii) minimal nonabelian subgroups have equal order, (c) maximal abelian subgroups have equal order, (d) every maximal abelian subgroup is contained in a minimal nonabelian subgroup and all maximal subgroups of any minimal nonabelian subgroup are maximal abelian in G. We prove the same results for metacyclic 2-groups (e) with abelian subgroup of index p, (f) without epimorphic image ? D8. The metacyclic p-groups containing (g) a minimal nonabelian subgroup of order p 4, (h) a maximal abelian subgroup of order p 3 are classified. We also classify the metacyclic p-groups, p > 2, all of whose minimal nonabelian subgroups have equal exponent. It appears that, with few exceptions, a metacyclic p-group has a chief series all of whose members are characteristic. 相似文献
3.
Ap-group of sufficiently large nilpotence class cannot occur as a normal subgroup contained in the Frattini subgroup of any
finite group. The Frattini subgroup of a group of order Π
pi
αi
with max α
i
at least 3, has nilpotence class at most 1/2 (max α
i
− 1). The Frattini subgroup of at-group is abelian. The occurrence of groups of orderp
4 as normal subgroups contained in Frattini subgroups is investigated.
National Science Foundation Science Faculty Fellow, University of Cincinnati 相似文献
4.
W. Mack Hill 《Israel Journal of Mathematics》1977,26(1):68-74
In the context of the problem of which nonabelianp-groups can occur as normal subgroups contained in Frattini subgroups, the family of supernilpotent groups (all maximal subgroups characteristic) is investigated. Results of this investigation are applied to the Frattini-embedding problem, incorporating recent work of A. R. Makan. The groups of order 2n (n ≦ 6) have been examined with respect to supernilpotence and their occurrence as normal subgroups contained in Frattini subgroups. Results of this examination are presented. 相似文献
5.
Wieferich pairs and Barker sequences 总被引:1,自引:0,他引:1
Michael J. Mossinghoff 《Designs, Codes and Cryptography》2009,53(3):149-163
We show that if a Barker sequence of length n > 13 exists, then either n = 189 260 468 001 034 441 522 766 781 604, or n > 2 · 1030. This improves the lower bound on the length of a long Barker sequence by a factor of more than 107. We also show that all but fewer than 1600 integers n ≤ 4 · 1026 can be eliminated as the order of a circulant Hadamard matrix. These results are obtained by completing extensive searches
for Wieferich prime pairs (q, p), which are defined by the relation qp-1 o 1{q^{p-1} \equiv1} mod p
2, and analyzing their results in combination with a number of arithmetic restrictions on n. 相似文献
6.
A. Schinzel 《Proceedings of the Steklov Institute of Mathematics》2012,276(1):250-256
A necessary and sufficient condition is given for an equation ax
m
+ bx
n
+ c = dy
p
+ ey
q
to have infinitely many rational solutions with a bounded denominator, under the assumption that m > n > 0, p > q > 0, ab ≠ 0 ≠ de and either m > p > 2, or m = p > 2 and n ≥ q. In a previous paper there was an additional assumption (m, n) = (p, q) = 1. 相似文献
7.
W. O. Alltop 《Israel Journal of Mathematics》1976,23(1):31-38
ItH
i
is a finite non-abelianp-group with center of orderp, for 1≦j≦R, then the direct product of theH
i
does not occur as a normal subgroup contained in the Frattini subgroup of any finitep-group. If the Frattini subgroup Φ of a finitep-groupG is cyclic or elementary abelian of orderp
2, then the centralizer of Φ inG properly contains Φ. Non-embeddability properties of products of groups of order 16 are established. 相似文献
8.
Explicit expressions for 4n + 2 primitive idempotents in the semi-simple group ring $R_{2p^{n}}\equiv \frac{GF(q)[x]}{p and q are distinct odd primes; n ≥ 1 is an integer and q has order
\fracf(2pn)2{\frac{\phi(2p^{n})}{2}} modulo 2p
n
. The generator polynomials, the dimension, the minimum distance of the minimal cyclic codes of length 2p
n
generated by these 4n + 2 primitive idempotents are discussed. For n = 1, the properties of some (2p, p) cyclic codes, containing the above minimal cyclic codes are analyzed in particular. The minimum weight of some subset of
each of these (2p, p) codes are observed to satisfy a square root bound. 相似文献
9.
The Agmon-Miranda maximum principle for the polyharmonic equations of all orders is shown to hold in Lipschitz domains in
ℝ3. In ℝn,n≥4, the Agmon-Miranda maximum principle andL
p-Dirichlet estimates for certainp>2 are shown to fail in Lipschitz domains for these equations. In particular if 4≤n≤2m+1 theL
p Dirichlet problem for Δ
m
fails to be solvable forp>2(n−1)/(n−3).
Supported in part by the NSF. 相似文献
10.
Haipeng QU 《Frontiers of Mathematics in China》2010,5(1):117-122
For a positive integer n, a finite p-group G is called an ℳ
n
-group, if all subgroups of index p
n
of G are metacyclic, but there is at least one subgroup of index p
n−1 that is not. A classical result in p-group theory is the classification of ℳ1-groups by Blackburn. In this paper, we give a slightly shorter and more elementary proof of this result. 相似文献
11.
LiQiongXU WeiMinXUE 《数学学报(英文版)》2003,19(1):141-146
Let n be an integer with |n| > 1. If p is the smallest prime factor of |n|, we prove that a minimal non-commutative n-insertive ring contains n
4 elements and these rings have five (2p+4) isomorphic classes for p = 2 (p ≠ 2).
This research is supported by the National Natural Science Foundation of China, and the Scientific Research Foundation for
“Bai-Qian-Wan” Project, Fujian Province of China 相似文献
12.
As a natural generalization of a restricted Lie algebra, a restricted Lie triple system was defined by Hodge. In this paper, we develop initially the Frattini theory for restricted Lie triple systems, generalize some results of Frattini p-subalgebra for restricted Lie algebras, obtain some properties of the Frattini p-subsystem and give the relationship between Фp(T) and Ф(T) for solvable Lie triple systems. 相似文献
13.
S Thangavelu 《Proceedings Mathematical Sciences》1990,100(2):147-156
The uniform boundedness of the Riesz means for the sublaplacian on the Heisenberg groupH
n is considered. It is proved thatS
R
α
are uniformly bounded onL
p(Hn) for 1≤p≤2 provided α>α(p)=(2n+1)[(1/p)−(1/2)]. 相似文献
14.
A Liep-algebraL is calledn-power closed if, in every section ofL, any sum ofp
i+n
th powers is ap
i
th power (i>0). It is easy to see that ifL isp
n
-Engel then it isn-power closed. We establish a partial converse to this statement: ifL is residually nilpotent andn-power closed for somen≥0 thenL is (3p
n
+2
+1)-Engel ifp>2 and (3 · 2
n+3+1)-Engel ifp=2. In particular, thenL is locally nilpotent by a theorem of Zel’manov. We deduce that a finitely generated pro-p group is a Lie group over thep-adic field if and only if its associated Liep-algebra isn-power closed for somen. We also deduce that any associative algebraR generated by nilpotent elements satisfies an identity of the form (x+y)
p
n
=x
p
n
+y
p
n
for somen≥1 if and only ifR satisfies the Engel condition.
This project was supported by the CNR in Italy and NSF-EPSCoR in Alabama during the first author’s stay at the Università
di Palermo. 相似文献
15.
On the generators of subgroups of unit groups of group rings 总被引:1,自引:0,他引:1
Ashwani K. Bhandari 《Bulletin of the Brazilian Mathematical Society》1990,20(2):87-93
In this paper we find the generators of a subgroup of finite index in the unit group of the integral group ring of the metacyclic
group of orderpq given byG=(a,x:a
p=1=x
q
,xax
−1=a
f
), wherep is an odd prime,q>2 a divisor ofp-1, andf belongs to the exponentq modulop. 相似文献
16.
Let w(x) = (1 - x)α (1 + x)β be a Jacobi weight on the interval [-1, 1] and 1 < p < ∞. If either α > ?1/2 or β > ?1/2 and p is an endpoint of the interval of mean convergence of the associated Fourier-Jacobi series, we show that the partial sum operators Sn are uniformly bounded from Lp,1 to Lp,∞, thus extending a previous result for the case that both α, β > ?1/2. For α, β > ?1/2, we study the weak and restricted weak (p, p)-type of the weighted operators f→uSn(u?1f), where u is also Jacobi weight. 相似文献
17.
J. Bourgain 《Israel Journal of Mathematics》1989,67(3):291-311
This paper is a follow up of [B1]. It is shown that the sequence of squares {n
2|n=1, 2, ...} contains Λ(p)-subsets of “maximal density”, for any givenp>4. The proof is based on the probabilistic method developed in [B1] and a precise estimate of the Λ(p)-constant for the sequence of squares itself. Analogues of this phenomenon are obtained for other arithmetic sets, such as
the sequence ofkth powers {n
k |n=1, 2, ...} or the sequence of prime numbers. Sections 2 and 3 of the paper are of independent interest to orthogonal system
theory. 相似文献
18.
Shandelle M. Henson 《Journal of Difference Equations and Applications》2013,19(3):315-331
The local existence and local asymptotic stability of nontrivial p-periodic solutions of p-periodically forced discrete systems are proven using Liapunov-Schmidt methods. The periodic solutions bifurcate transcritically from the trivial solution at the critical value n=ncr of the bifurcation parameter with a typical exchange of stability. If the trivial solution loses (gains) stability as n is increased through ncr , then the periodic solutions on the nontrivial bifurcating branch are locally asymptotically stable if and only if they correspond to n>ncr (n ncr ). 相似文献
19.
Filippo Gazzola Hans-Christoph Grunau 《Calculus of Variations and Partial Differential Equations》2007,30(3):389-415
We are interested in stability/instability of the zero steady state of the superlinear parabolic equation u
t
+ Δ2
u = |u|
p-1
u in , where the exponent is considered in the “super-Fujita” range p > 1 + 4/n. We determine the corresponding limiting growth at infinity for the initial data giving rise to global bounded solutions.
In the supercritical case p > (n + 4)/(n−4) this is related to the asymptotic behaviour of positive steady states, which the authors have recently studied. Moreover,
it is shown that the solutions found for the parabolic problem decay to 0 at rate t
−1/(p-1). 相似文献
20.
J. R. Morrow 《Israel Journal of Mathematics》1978,29(2-3):199-204
It is proved that in anF-space with a basis (χ
n
)
n
= 1/∞
, (χ
n
)
n
= 1/∞
is equivalent to the unit-vectors basis ofc
0,l
p (p>0), or (s) if and only if (χ
n
)
n
= 1/∞
is equivalent to each of itsɛ-normalized block basic sequences for eachɛ>0. This result is an extension of a theorem of M. Zippin. 相似文献