Quasithin Groups

Abstract

The treatment of quasithin groups of characteristic 2 was one of the last steps in the Classification of the finite simple groups. Geoff Mason [12] announced a classification of these groups in about 1980, but never published his work. A few people have a copy of a large manuscript containing his efforts, but because it was distributed slowly, section by section, it was only during the last few years that it was realized that Mason’s manuscript is incomplete in various ways. A few years ago I wrote up a treatment which begins where Mason’s manuscript ends and finishes the problem assuming the results he says he proves. I have only read Mason’s manuscript superficially, but it appears there are missing lemmas even for the part of the problem the theorems in his manuscript cover. I do believe however that he has seriously addressed the issues involved and that he could turn his manuscript into a proof with enough work. However Mason is now involved with Moonshine and has no interest in completing or publishing his manuscript.