Recognition of finite exceptional groups of Lie type. (Q2790727)

Part of the constructive recognition project is to provide algorithms which construct explicit isomorphisms between a (finite) quasisimple group \(G\) and a so-called standard copy of \(G\). Such algorithms are known for many of the classical quasisimple groups, and the present paper considers the case of the exceptional groups of Lie type.NEWLINENEWLINE Let \(G\) be an absolutely irreducible subgroup of \(\mathrm{GL}_d(F)\) over a finite field \(F\) of characteristic \(p\), and suppose that \(G\cong G(q)\) where \(G(q)\) is a quasisimple group of exceptional Lie type and \(q>2\) is a power of \(p\). Suppose further that \(G(q)\) is not a Suzuki or Ree group and that \(G(q)\neq{^3D_4(q)}\) if \(q\) is even. Then the authors describe a Las Vegas algorithm that constructs an isomorphism (and its inverse) from \(G\) onto a standard copy of \(G(q)\) modulo a central subgroup. The algorithm is shown to run in polynomial time, assuming the existence of a specific discrete log oracle. It has been implemented in Magma.