Interpr\´etation de l´Arithm\´etique dans certains groupes de permutations affines par morcea

The Arithmetic is interpreted in all the groups of Richard Thompson and nGraham Higman, as well as in other groups of piecewise affine permutations of nan interval which generalize the groups of Thompson and Higman. In particular, nthe elementary theories of all these groups are undecidable. Moreover, nThompson s group F and some of its generalizations interpret the Arithmeti..