TITLE

Some Elements of Finite Order in K 2â„š

AUTHOR(S)
Cheng, Xiao Yun; Xia, Jian Guo; Qin, Hou Rong
PUB. DATE
May 2007
SOURCE
Acta Mathematica Sinica;May2007, Vol. 23 Issue 5, p819
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
Let K 2 be the Milnor functor and let Φ n ( x) ∈ ℚ[ x] be the n-th cyclotomic polynomial. Let G n (ℚ) denote a subset consisting of elements of the form { a,Φ n ( a)}, where a ∈ ℚ*. and {, } denotes the Steinberg symbol in K 2ℚ. J. Browkin proved that G n(ℚ) is a subgroup of K 2ℚ if n = 1, 2, 3, 4 or 6 and conjectured that G n (ℚ) is not a group for any other values of n. This conjecture was confirmed for n = 2 r 3 s or n = p r , where p ≥ 5 is a prime number such that h(ℚ(ζ p )) is not divisible by p. In this paper we confirm the conjecture for some n, where n is not of the above forms, more precisely, for n = 15, 21, 33, 35, 60 or 105.
ACCESSION #
24718800

 

Related Articles

  • Relative $K_{0}$, annihilators, Fitting ideals and Stickelberger phenomena. Victor P. Snaith // Proceedings of the London Mathematical Society;May2005, Vol. 90 Issue 3, p545 

    When $G$ is abelian and $l$ is a prime we show how elements of the relative K-group $K_{0}({\bf Z}_{l}[G], {\bf Q}_{l})$ give rise to annihilator/Fitting ideal relations of certain associated ${\bf Z}[G]$-modules. Examples of this phenomenon are ubiquitous. Particularly, we give examples in...

  • Mathemimetics I: Self-computational prime-number line and three-dimensional Diophantine equation matrix. Trell, Erik // AIP Conference Proceedings;Sep2012, Vol. 1479 Issue 1, p2138 

    Emulating Nature by observation and ground-up application of its patterns, structures and processes is a classical scientific practice which under the designation of Biomimetics has now been brought to the Nanotechnology scale where even highly complex systems can be replicated by continuous or...

  • On the finiteness and non-existence of certain mod 2 Galois representations of quadratic fields. Moon, Hyunsuk; Taguchi, Yuichiro // AIP Conference Proceedings;1/22/2008, Vol. 976 Issue 1, p169 

    Some finiteness and non-existence results are proved of 2-dimensional mod 2 Galois representations of quadratic fields unramified outside 2.

  • THE UNIQUENESS OF THE PRIME MARKOFF NUMBERS. BUTTON, J. O. // Journal of the London Mathematical Society;08/01/1998, Vol. 58 Issue 1, p9 

    Given the Diophantine equation a2+b2+c2=3abc, a solution triple of natural numbers (a, b, c) can be arranged in ascending order so that adbdc. Then, given the largest element c, one can ask whether this uniquely determines the triple. This is referred to as the Markoff conjecture. The paper...

  • On the system of Diophantine equations x² - 6y² = 1 and y² - Dz² = 4. DU Xiancun; GUAN Xungui; YANG Huizhang // Journal of Huazhong Normal University;Jun2014, Vol. 48 Issue 3, p310 

    Let p1, ⋯, ps (1≤ s ≤ 4) are distinct odd primes. In this paper, we proved that if D = 2 p1 ⋯ ps, 1 ≤ s ≤ 4, then the system x² - 6y² = 1 and y² - Dz² = 4 has only trivial solution (x, y, z) = (±5, ±2,0) with the exception that D = 2 x 11 x 97.

  • On exponential sums of digital sums related to Gelfond's theorem. Okada, Tatsuya; Kobayashi, Zenji; Sekiguchi, Takeshi; Shiota, Yasunobu // AIP Conference Proceedings;1/22/2008, Vol. 976 Issue 1, p176 

    In this paper, we first give explicit formulas of exponential sums of sum of digits related to Gelfond's theorem. As an application of these formulas, we obtain a simple expression of Newman-Coquet type summation formula related to the number of binary digits in a multiple of a prime number.

  • On the Farrell—Jones Conjecture and its applications. Bartels, Arthur; Lück, Wolfgang; Reich, Holger // Journal of Topology;Jan2008, Vol. 1 Issue 1, p57 

    We present the status of the Farrell–Jones Conjecture for algebraic K-theory for a group G and arbitrary coefficient rings R. We add new groups for which the conjecture is known to be true, and we study inheritance properties. We discuss new applications, focussing on the Bass Conjecture,...

  • EXCEPTIONAL OBJECTS IN HEREDITARY CATEGORIES. RINGEL, CLAUS MICHAEL // Analele Stiintifice ale Universitatii Ovidius Constanta: Seria M;2015, Vol. 23 Issue 1, p150 

    Let k be a field and A a finite dimensional k-category which is a hereditary length category. We are going to show that the support algebra of any object of A without self-extension is a finite dimensional k-algebra. An object in A is said to be exceptional provided it is inde-composable and has...

  • SYMBOL LENGTHS IN MILNOR K-THEORY. Becher, Karim Johannes; Hoffmann, Detlev W. // Homology, Homotopy & Applications;2004, Vol. 6 Issue 1, p17 

    Let F be a field and p a prime number. The p-symbol length of F, denoted by λp(F), is the least integer l such that every element of the group K2F/pK2F can be written as a sum of ≤ l symbols (with the convention that λp (F) = ∞ if no such integer exists). In this article, we...

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics