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We calculate the rank gradient and p-gradient of free products, free productswith amalgamation over an amenable subgroup, and HNN extensions with anamenable associated subgroup. The notion of cost is used to compute the rankgradient of amalgamated free products and HNN extensions. For the p-gradientthe Kurosh subgroup theorems for amalgamated free products and HNN extensionswill be used.

Rank gradient and p-gradient of amalgamated free products and HNN extensions