On acylindrical hyperbolicity of groups with positive first 2-Betti number

rifa rifdah awaliyah;

We prove that every finitely presented group with positive first 2-Betti number that virtually surjects onto Z is acylindrically hyperbolic. In particular, this implies acylindrical hyperbolicity of finitely presented residually finite groups with positive first 2-Betti number as well as groups of deficiency at least 2.