This thesis deals ~.;.lth the following problem: given n a f-fnite

zbelian group, compute '.V (Zn). Here %(R) = K e r ( Y ( R [ t l ) -+%(R)) 1=

whwe -the i~q is that i'?d1icp3J by a~>gnz;~tation. ZnP p ~ u p ~ ( Z T 1

a p p ~ ~ ~ s as a direct- s m ~ d b. the soup ij (B' - 1 where IT' is

finitely torsiorr pa r t of

calculations consist of t ~ ~ o parts. In the f k s t pwt- it 2s

sho'7wi-1 thzt fi%ii(Zrr) -- = o f i r ~ IT of square free order. In the secor.d

~v '? shad t h a t otkenwise the g m ~ ~ Prjr (22 l can. be. infinite. In par- '1 - 2 ticu4ar w e show t'mt if I >p p d d and IT c y c l i c then

(P (P 1

In addition several general facts abut NKl and NK2'are also proved

and ut i l i z sd -h these comp~,taPioils. The foll-owing results are of

i.ndepwIdw~t interest.

induces a smject!~on NK ( Z i r ) -+WdL(~~'l I =

Some ot:+er exaigles me given wher~e. The hyptheses uf the -th?o?sns

proved csnn.3~ 52 wsdilce-n?d a ~ d cexea-in other examples for. irifij?i-te