The \(P!\)-theorem
Recall that a group \(H\) is of characteristic \(p\) if \(C_H(O_p(H))\leq O_p(H)\) and is of local characteristic \(p\) if every \(p\)-local subgroup has characteristic \(p\). This paper is part of the project initiated by Meierfrankenfeld to classify all finite groups of local characteristic \(p\) that do not have a strongly embedded \(p\)-group. This is part of a proposed third generation proof of the classification of finite simple groups (and so of course one is not allowed to use the classification -- on the other hand, by assuming that the group is a minimal counterexample to the classification, one can assume that all proper sections of the group involve only the known simple groups). This is a difficult and deep paper and relies heavily on the amalgam method. The results and hypotheses are too technical to describe here. We refer the reader to the article and the references quoted there.
scientific article; zbMATH DE number 1924680