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Abstract
We calculate the rank gradient and p-gradient of free products with amalgamation over an amenable subgroup and HNN extensions with an amenable associated subgroup. The notion of cost is used to compute the rank gradient of amalgamated free products and HNN extensions. For the p-gradient the Kurosh subgroup theorems for amalgamated free products and HNN extensions will be used.
ACKNOWLEDGMENTS
The author would like to thank his advisor, Mikhail Ershov, for his help with the present material and also with his helpful comments on earlier drafts of this paper. The author would also like to thank the anonymous referee for suggesting an improvement to Proposition 3.5.
Notes
Communicated by A. Olshanskii