Lacunary hyperbolic groups with fast injectivity radius growth and enough loxodromic elements are selfless

Goulnara Arzhantseva, Martin Finn-Sell

We prove that a lacunary hyperbolic group $G=\underrightarrow{\lim }{G}_i$ with sufficient generics is selfless in the sense of Amrutam--Gao--Kunnawalkam Elayavalli--Patchell, provided the hyp…