We set and . Let be the Fermat hypersurface of degree in the projective space . It is known that the automorphism group of contains a subgroup which is isomorphic to . Let be a subgroup of the projective linear group such that is isomorphic to . We show that can be lifted into a subgroup of the general linear group except for the cases where and . As a result, we show that for a smooth hypersurface in of degree , if acts faithfully on , then is the Fermat hypersurface unless and .
"CHARACTERIZATION OF FERMAT HYPERSURFACES BY ABELIAN GROUPS." J. Commut. Algebra 15 (2) 233 - 248, Summer 2023. https://doi.org/10.1216/jca.2023.15.233