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 = 2r3s 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.
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This work is supported by SRFDP, the 973 Grant, the National Natural Science Foundation of China 10471118 and the Jiangsu Natural Science Foundation Bk2002023
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Cheng, X.Y., Xia, J.G. & Qin, H.R. Some Elements of Finite Order in K 2ℚ. Acta Math Sinica 23, 819–826 (2007). https://doi.org/10.1007/s10114-005-0852-6
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DOI: https://doi.org/10.1007/s10114-005-0852-6