  The aim of this paper is to describe all definable subgroups of SL2(K), for K
a p-adically closed field. We begin by giving some "frame subgroups" which
contain all nilpotent or solvable subgroups of SL2(K). A complete description
is givien for K a p-adically closed field, some results are generalizable to K
a field elementarily equivalent to a finite extension of Qp and an almost
complete description is given for Q an p . We give also some indications about
genericity and generosity in SL2(K).
