@article{20603,
  abstract     = {We study the growth of sumsets A+B⊂S⊂G, where S does not contain an arithmetic progression of length 2k+1, and where G is a commutative group, in which every nonzero element has an order of at least 2k+1. More specifically, we show the following: if A,B⊂G are sets such that A+B does not contain an arithmetic progression of length 2k+1, then
|A+B|≥|A|2k−13k−2|B|k3k−2.
As an application we derive upper bounds on the cardinality of the summands in sumsets A+B+C contained in the set of t-th powers, where t≥2 is an integer. In particular, we show that min(|A|,|B|,|C|)≪(logN)4/5 for t=2, and min(|A|,|B|,|C|)≪t(logN)1/2 for t≥3.},
  author       = {Elsholtz, Christian and Ruzsa, Imre Z. and Wurzinger, Lena},
  issn         = {1730-6264},
  journal      = {Acta Arithmetica},
  pages        = {289--303},
  publisher    = {Institute of Mathematics},
  title        = {{Sumset growth in progression-free sets}},
  doi          = {10.4064/aa250115-14-7},
  volume       = {220},
  year         = {2025},
}