A theorem of Hall-Higman type for groups of odd order (Q1123258)

Extending previous work by the author, the following quite general theorem of Hall-Higman type for groups of odd order over the complex field is obtained: Theorem. Let ARP be a group of odd order, where: (i) \(P\triangleleft ARP\) is an extraspecial p-group, Z(P)\(\leq Z(ARP)\). (ii) \(R\triangleleft AR\) is an r-group, \(r\neq p\). (iii) \((| A|,rp)=1\). (iv) \(C_ A(P)=1\) and \(C_ A(R/C_ R(P))\) is nilpotent and \(C_ q\wr C_ q\)-free for all q. Let V be a complex ARP-module, nontrivial for Z(P). Then \(V_ A\) contains the regular A-module.