DIVISIBLE ELEMENTS IN HOMOLOGY OF THE GENERAL
                        LINEAR GROUP OF A NUMBER FIELD



                   D.Arlettaz, P. Zelewski




Let D(n) denote the subgroup of the integral homology  H_{n}(SL(F)) , where F 
denotes a number field, consisting of elements that are infinitely divisible.
We prove that D(n) is finite, that for F-totally real it is in genaral 
non-trivial (we provide an explicit lower bound on its order expressed in 
terms of the zeta function of F ) and we show certain "vanishing 
theorem " for D(n) with hypothesis depending on the Kummer-Vandiver conjecture.
We state few problems that we were unable to solve cocerning the structure 
of H_{*}(SL(F)). 
The paper contains 9 pages.