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

Definable subgroups in $SL\_2$ over a p-adically closed field