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
DOC. TYPE
Article
ABSTRACT
Let K 2 be the Milnor functor and let Î¦ n ( x) âˆˆ â„š[ x] be the n-th cyclotomic polynomial. Let G n (â„š) denote a subset consisting of elements of the form { a,Î¦ n ( a)}, where a âˆˆ â„š*. and {, } denotes the Steinberg symbol in K 2â„š. J. Browkin proved that G n(â„š) is a subgroup of K 2â„š if n = 1, 2, 3, 4 or 6 and conjectured that G n (â„š) 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 â‰¥ 5 is a prime number such that h(â„š(Î¶ 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

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