On the group cohomology of the semi-direct product Zn⋊ρZ/m and a conjecture of Adem–Ge–Pan–Petrosyan

AbstractConsider the semi-direct product Zn⋊ρZ/m. A conjecture of Adem–Ge–Pan–Petrosyan predicts that the associated Lyndon–Hochschild–Serre spectral sequence collapses. We prove this conjecture provided that the Z/m-action on Zn is free outside the origin. We disprove the conjecture in general, namely, we give an example with n=6 and m=4, where the second differential does not vanish