This publication presents the most essential portions of the author's German Diplomarbeit of 1984 [2] and a "sprinkling" of some new considerations and results as well which earnestly try to propose coming directions for the (timeless and eternal) Sylow theory in (locally) finite groups (see the pages 14, 15, 20 and 24 to 34). The Mathematics edition extracts from the Full edition (see ISBN 978-3-7568-0801-4) all the very beautiful mathematical content. The Line numbering is facilitating and shall lively encourage (Scholarly Peer) Review. The First update considered comments by the author and an unknown referee. The Second update considers improvements of the Second edition of the Full edition and of the First Trilogy (see ISBN 978-3-7504-0398-7).

Felix F. Flemisch proudly received his degree Bacc.Math. in 1974 from the Albert-Ludwigs-Universität at lovely Freiburg im Breisgau, his degree M.Sc. in 1975 from the University of London, and finally his degree Dipl.-Math. at so marvellous Freiburg i.Br. in 1985. From February 1981 until April 1985 he was affiliated to the Albert-Ludwigs-Universität Freiburg im Breisgau, Universitätsklinikum Freiburg, Institut für Medizinische Biometrie und Statistik (IMBI). Since May 1985 he was working for the telecom industry. Since October 2016 he is retired.