Some Elements of Finite Order in K 2.

Let K 2 be the Milnor functor and let . n (x) . .[x] be the n-th cyclotomic polynomial. Let G n (.) denote a subset consisting of elements of the form {a,. n (a)}, where a . .*. and {, } denotes the Steinberg symbol in K 2.. J. Browkin proved that G n(.) is a subgroup of K 2. if n = 1, 2, 3, 4 or 6 and conjectured that G n (.) 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(.(. 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.