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We study the (Ahlfors regular) conformal dimension of the boundary atinfinity of Gromov hyperbolic groups which split over elementary subgroups. Ifsuch a group is not virtually free, we show that the conformal dimension isequal to the maximal value of the conformal dimension of the vertex groups, or1, whichever is greater, and we characterise when the conformal dimension isattained. As a consequence, we are able to characterise which Gromov hyperbolicgroups (without $2$-torsion) have conformal dimension 1, answering a questionof Bonk and Kleiner.

Conformal dimension of hyperbolic groups that split over elementary subgroups