Schlagworte: conjugacy of maximal (i.e. Sylow) p-subgroups; singular p-subgroup; locally finite group satisfying the (strong) Sylow Theorem for the prime p (or the [strong] Sylow p-Theorem) (G « Syl-p);, finite simple group; split sequence of finite p-perfect subgroups; (very) good Sylow p-subgroup; p-uniqueness subgroup; singular Sylow p-subgroup; minimal p-unique subgroup;, (proper) Sylow p-intersection; the (numerical) Sylow p-invariants 1) p-uniqueness and 2) Sylow p-intersection; split sequence of finite p-perfect subgroups;, Sylow-separated sequence of p-subgroups; maximum conditions (for IpG and for the Sylow-separated sequences of p-subgroups);, locally finite group G satisfying the minimum condition for p-subgroups (G « Min-p)
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 first degree Bacc.Math. in 1974 from the Albert-Ludwigs-Universität at so lovely Freiburg im Breisgau, his degree M.Sc. in 1975 from the University of London, UK, and finally his degree Dipl.-Math. at fabulous Freiburg i.Br. in 1985. From February 1981 until April 1985 he was quite happily affiliated to the esteemed Albert-Ludwigs-Universität Freiburg i.Br., Universitätsklinikum Freiburg, Institut für Medizinische Biometrie und Statistik (IMBI). Since May 1985 he was enthusiastically with great joy working for the telecom industry. On April 11, 1992, he married beloved Helga in beautiful Florence in Tuscany in Italy. Since October 2016 he is retired and is still resp. is again loving mathematics and above all the beautiful group theory.
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