Recurrent random walks on certain classes of groups

This article is divided into two parts: in the first we give some results about renewal and normality of a recurrent random walk (r.w.) on an abelian group, without the Harris hypothesis, which will extend the theorems of S.C. Port and C.J. Stone (8]) to a larger class of functions. They are stated in the Theorems 1.14 and 1.15. The technique will be to approximate the recurrent r.w. by a Harris recurrent r.w., for which the recent results of A. Brunel and D. Revuz (2–4]) hold.the second part the results of the first part are extended to a particular class of nonabelian groups.The author wishes to thank A. Brunel for several very useful conversations and suggestions.