Pushing up \(Sp(4,q)\), q odd
The author handles the pushing-up situation for \(Psp(4,p^ n)\), p odd. Let M be a finite group, p a prime, S a Sylow p-subgroup of M. Assume that no nontrivial characteristic subgroup of S is normal in M and \((M/O_ p(M))/\Phi (M/O_ p(M))\cong PSp(4,p^ n)\), p odd. Set \(\tilde M=O^ p(M)\) and \(V=O_ p(\tilde M)\). Assume \(O_ p(M)=1\). Then either \(\tilde M\cong PSp(4,p^ n)\) or \(\tilde M/V\cong Sp(4,p^ n)\) and V is the natural \(Sp(4,p^ n)\)-module. As in his papertreating the even characteristic [ibid. 112, 430-466 (1988; reviewed above)] the author uses the amalgam-method to prove his result. But by lack of strange examples the proof is much easier.
scientific article; zbMATH DE number 4036054