Appears in collection : Model theory of valued fields / Théorie des modèles des corps valués

(joint with Yatir Halevi and Assaf Hasson) We continue our study of interpretable groups in various valued fields (e.g. RCVF, ACVF and $p$-adically closed fields), and show that if $G$ is an interpretable definably semisimple group, namely has no definable infinite normal abelian subgroup, then, up to a finite index subgroup, it is definably isogenous to a $G_1 \times G_2$, where $G 1$ and $G 2$ are $K$-linear and $k$-linear groups, respectively $(K=$ the valued field and $k=$ the residue field). As in our previous works, we analyze the groups via the 4 distinguished sorts: $K, k, \Gamma$ (value group) and $K / \mathcal{O}$ (the closed 0 -balls), and show that the sorts $\Gamma$ and $K / \mathcal{O}$ do not appear when $G$ is definably semisimple.