Finite group actions on \(P^ 2({\mathbb{C}})\) (Q1112177)

The main result of the paper is the following: Let G be a finite group with a locally linear action on \({\mathbb{P}}^ 2({\mathbb{C}})\) (i.e. such that each singular point has an invariant neighbourhood which is equivariantly homeomorphic to a neighbourhood of O in a (real) representation space). If G induces the indentity on homology, then G is isomorphic to a subgroup of \(PGL_ 3({\mathbb{C}})\). (A list of such subgroups of \(PGL_ 3({\mathbb{C}})\) see in \textit{G. Miller}, \textit{H. B. Lichfeldt}, \textit{L. Dickson}, Theory and applications of finite groups (1916).)