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1.
Let E/F be a Galois extension of number fields with the quaternion Galois group Q 8. In this paper, we prove some relations connecting orders of the odd part of the kernel of the transfer map of the tame kernel of E with the same orders of some of its subfields. Let E/? be a Galois extension of number fields with the Galois group Q 8 and p an odd prime such that p ≡ 3 (mod 4). We prove that if there is at most one quadratic subfield such that the p-Sylow subgroup of the tame kernel is nontrivial, then p r -rank(K 2(E/K)) is even, i.e., 2|p r -rank(K 2(𝒪 E )) ? p r -rank(K 2(𝒪 K )), where K is the quartic subfield of E. 相似文献
2.
We define a particular type of automorphisms called transvections on a finite finite abelian p-group Hp. It is proved that the subgroup E of the automorphism group Aut(Hp) of Hp generated by those transvections is normal in it, and that Aut(Hp) can be written as the product of E and some abelian subgroup K. The center of Aut(Hp) is also determined. 相似文献
3.
We characterize all equivariant odd spectral triples for the quantum SU(2) group acting on its L
2-space and having a nontrivial Chern character. It is shown that the dimension of an equivariant spectral triple is at least three, and given any element of the K-homology group of SUq(2), there is an equivariant odd spectral triple of dimension 3 inducing that element. The method employed to get equivariant spectral triples in the quantum case is then used for classical SU(2), and we prove that for p < 4, there does not exist any equivariant spectral triple with nontrivial K-homology class and dimension p acting on the L
2-space.The first author would like to acknowledge support from the National Board of Higher Mathematics, India. 相似文献
4.
Qin-hai ZHANG Cui-juan SUN Hai-peng QU & Ming-yao XU School of Mathematics Computer Sciences Shanxi Normal University Linfen China 《中国科学A辑(英文版)》2007,50(6):814-820
Following Blackburn, Deaconescu and Mann, a group G is called an equilibrated group if for any subgroups H,K of G with HK = KH, either H≤NG(K) or K≤NG(H). Continuing their work and based on the classification of metacyclic p-groups given by Newman and Xu, we give a complete classification of 2-generator equilibrated p-groups in this note. 相似文献
5.
Wojciech Gajda 《K-Theory》2001,23(4):323-343
We apply the recently proven compatibility of Beilinson and Soulé elements in K-theory to investigate density of rational primes p, for which the reduction map K
2n+1() K{2n+1}(Fp)is nontrivial. Here n is an even, positive integer and Fp denotes the field of p elements. In the proof we use arithmetic of cyclotomic numbers which come from Soulé elements. Divisibility properties of the numbers are related to the Vandiver conjecture on the class group of cyclotomic fields. Using the K-theory of the integers, we compute an upper bound on the divisibility of these cyclotomic numbers. 相似文献
6.
7.
The aim of this article is to investigate the autotopism group of a semifield of order p 4, p is an odd prime, admitting a four-group of automorphisms E? Z 2 × Z 2 acting freely on A. 相似文献
8.
Qin Yue 《K-Theory》2005,35(1-2):69-91
Let
and
, d1 and d2 squarefree integers, be an imaginary field and a biquadratic field, respectively. Let S be the set consisting of all infinite primes, all dyadic primes and all finite primes which ramify in E. Suppose the 4-rank of the class group of F is zero and the S-ideal class group of F has odd order, we give the forms of all elements of order ⩽ 2 in K2OE and use the Hurrelbrink and Kolster’s method [Hurrelbrink, J. and Kolster, M.: J. reine angew. Math. 499 (1998), 145–188] to obtain the forms of all elements of order 4 in K2OE.
Received: September 2004 相似文献
9.
Glaz and Wickless introduced the class G of mixed abelian groups A which have finite torsion-free rank and satisfy the following three properties: i) A
p is finite for all primes p, ii) A is isomorphic to a pure subgroup of
P
A
P and iii) Hom(A, tA) is torsion. A ring R is a left Kasch ring if every proper right ideal of R has a non-zero left annihilator. We characterize the elements A of G such that E(A)/tE(A) is a left Kasch ring, and discuss related results. 相似文献
10.
Pete L. Clark 《Journal of Number Theory》2005,114(1):193-208
Let E/K be an elliptic curve defined over a number field, and let p be a prime number such that E(K) has full p-torsion. We show that the order of the p-part of the Shafarevich-Tate group of E/L is unbounded as L varies over degree p extensions of K. The proof uses O’Neil's period-index obstruction. We deduce the result from the fact that, under the same hypotheses, there exist infinitely many elements of the Weil-Châtelet group of E/K of period p and index p2. 相似文献
11.
Let be a 2‐factorization of the complete graph Kv admitting an automorphism group G acting doubly transitively on the set of vertices. The vertex‐set V(Kv) can then be identified with the point‐set of AG(n, p) and each 2‐factor of is the union of p‐cycles which are obtained from a parallel class of lines of AG(n, p) in a suitable manner, the group G being a subgroup of A G L(n, p) in this case. The proof relies on the classification of 2‐(v, k, 1) designs admitting a doubly transitive automorphism group. The same conclusion holds even if G is only assumed to act doubly homogeneously. © 2006 Wiley Periodicals, Inc. J Combin Designs 相似文献
12.
New examples of <Emphasis Type="Italic">c</Emphasis><Subscript>0</Subscript>-saturated Banach spaces
I. Gasparis 《Mathematische Annalen》2009,344(2):491-500
For every p ∈ (1, ∞), an isomorphically polyhedral Banach space E
p
is constructed which has an unconditional basis and does not embed isomorphically into a C(K) space for any countable and compact metric space K. Moreover, E
p
admits a quotient isomorphic to ℓ
p
. 相似文献
13.
Let KGbe the group algebra of a p1 -group Gover a field Kof characteristic p > 0, and let U(KG)be its group of units. If KGcontains a nontrivial bicyclic unit and if Kis not algebraic over its prime field, then we prove that the free product Zp? Zp? Zpcan be embedded in U(KG). 相似文献
14.
Douglas R. Anderson 《K-Theory》1990,4(6):569-590
Let Z be a boundedness control space and p: X Z be a continuous map. The boundedly controlled Whitehead group Wh
bc
(X, p) is defined to be a quotient of the boundedly controlled K
1-group K
1
bc
(X, p) by a certain subgroup whose generators are explicitly given. In general, little is known about this subgroup and it is even possible that it vanishes; i.e. that the boundedly controlled K
1 and Whitehead groups are identical. This paper examines the structure of this subgroup in the case when p is the open cone on a PL map between compact polyhedra. As a byproduct, it calculates Wh
bc
(X, p) in some of these cases.Partially supported by the NSF under grant number DMS-8803149. 相似文献
15.
A subgroup H of a group G is called µ-supplemented in G if there exists a subgroup K such that G = HK and H 1 K is a proper subgroup in G for every maximal subgroup H 1 in H. For the initial values of p, we establish the p-supersolubility of a finite group with a μ-supplemented Sylow p-subgroup. 相似文献
16.
Kazuya Kato 《K-Theory》2005,34(2):99-140
We compute K1 of completed group rings of some two dimensional p-adic Lie groups.
Dedicated to Professor Spencer Bloch on his sixtieth birthday 相似文献
17.
18.
We prove that there is a Poincaré type duality in E-theory between higher rank graph algebras associated with a higher rank graph and its opposite correspondent. We obtain an
r-duality, that is the fundamental classes are in Er. The basic tools are a higher rank Fock space and higher rank Toeplitz algebra which has a more interesting ideal structure
than in the rank 1 case. The K-homology fundamental class is given by an r-fold exact sequence whereas the K-theory fundamental class is given by a homomorphism. The E-theoretic products are essentially pull-backs so that the computation is done at the level of exact sequences.
Mathematics Subject Classification (2000): 46L80. 相似文献
19.
H. Markšaitis 《Lithuanian Mathematical Journal》2000,40(1):39-47
LetK
p (p, q) be the maximalp-extension of the field ℚ of rational numbers with ramification pointsp andq. LetG
p (p, q) be the Galois group of the extensionK
p(p.q)/ℚ. It is known thatG
p(p, q) can be presented by two generators which satisfy a single relation. The form of this relation is known only modulo
the second member of the descending central series ofG
p(p, q). In this paper, we find an arithmetical-type condition on which the form of the relation modulo the third member of
the descending central series ofG
p(p, q) depends. We also consider two examples withp=3,q=19 andp=3,q=37.
Translated from Lietuvos Matematikos Rinkinys, Vol. 40, No. 1, pp. 48–60, January–March, 2000.
Translated by H. Markšaitis 相似文献
20.
The purpose of this paper is to exhibit a new family of real bicyclic biquadratic fields K for which we can write the Hasse unit index of the group generated by the units of the three quadratic subfields in the unit
group E
K
of K. As a byproduct, one can explicitly relate the class number of K with the product of the class numbers of the three quadratic subfields.
Received: 25 July 2000 / Revised version: 12 December 2000 相似文献