The Strong Sylow Theorem for the Prime p in Simple Locally Finite Groups– De Luxe Edition

Abstract

This Research Article extends the JMCA Research Article “The Strong Sylow Theorem for the Prime p in Simple Locally Finite Groups” (see https://www.onlinescientificresearch.com/articles/the-strong-sylow-theorem-for-the-prime-p-in-simple-locally-finitegroups.pdf ) from 71 pages to 220 pages by adding Pages i to viii, -1 to -18, 72 to 266, and ix to x (see Page v).
Pages i to -18 start with this Abstract and then honour Prof. Otto H. Kegel’s beautiful paper [44] thereby explaining its relationship to its main result and to the 71-pages Research Article, and commenting on its final considerations. They then give an overview of the 220-pages Research Article, including the Front Cover and a Table of Contents, and explain in great detail the relationships of the 71-pages Research Article to JMCA and to the Ischia Group Theory (IGT) 2024 Conference and its upcoming Proceedings, centred around the Talk given by the author at the Conference on April 11, the 100th birthday of Prof. Philip Hall. They close with a List of Open Issues some of which the author has solved already in yet unpublished work.
Pages 72 to x start with a dedication to Helga (see Page 15), continue with the PowerPoint Presentation at IGT 2024, honour Ludvig M. Sylow, the discoverer and explorer of Sylow Theory, recall that Ischia was twice an Artist Colony, remember Philip Hall’s and Graham Higman’s fundamental paper “On the p-Length of p-Soluble Groups and Reduction Theorems for Burnside’s Problem” thereby explaining its relationship to the 71-pages Research Article, recall Some Historicals on Group Theory, in particular Philip Hall’s hand-written Lecture Notes on Group Theory and show these beautiful Lecture Notes, show a presentation of WIKIPEDIA’s Classification of finite simple groups, remember Prof. Kegel and Prof. Hall at the Mathematisches Forschungsinstitut Oberwolfach (MFO), and finally as Back Cover refer to Philip Hall’s Archive at the London Mathematical Society and again to his Lecture Notes, and close by showing Who is Felix F. Flemisch ? & Another Abstract of the 71-pages Research Article.