Classification of non-solvable groups whose power graph is a cograph

Abstract In recent work, Cameron, Manna and Mehatari have studied the finite groups whose power graph is a cograph, which we refer to as power-cograph groups. They classify nilpotent with this property, they establish partial results in general setting, highlighting certain number-theoretic difficulties that arise for simple of form PSL 2 ⁡ ( q stretchy="false">) \operatorname{PSL}_{2}(q) or Sz ⁢ e + 1 \operatorname{Sz}(2^{2e+1}) . paper, prove these problems are fact only obstacles classification non-solvable Specifically, case, give terms such isomorphic For solvable able precisely describe structure We obtain complete Gruenberg–Kegel connected. Moreover, reduce case where disconnected