Finite Groups With Automorphisms Inverting Many Elements

Finite Groups with Automorphisms Inverting Many Elements

Finite Groups Whose 2-Subgroups Are Generated by at Most 4 Elements

The object of the memoir is to determine all finite simple (and more generally fusion-simple) groups each of whose 2-subgroups can be generated by at most 4 elements. Using a result of MacWilliams, we obtain as a corollary the classifications of all finite simple groups whose Sylow 2-subgroups do not possess an elementary abelian normal subgroups of order 8. The general introduction provides a fairly detailed outline of the over-all proof of our main classification theorem, including the methods employed. The proof itself is divided into six major parts; and the introductory section of each part gives a description of the principal results to be proved in that part.

An Analysis of Finite Groups with Automorphisms Inverting Most Group Elements