The Strong Sylow Theorem for the Prime p in Projective Special Linear Locally Finite Groups - Part 3 of a Trilogy

Manuscript on Sylow theory in locally finite groups - Part 3 of a Trilogy

Dipl.-Math. Felix F. Flemisch (Autor)

Buch | Hardcover

48 Seiten

2023 | 2. Auflage
BoD – Books on Demand (Verlag)
9783757860011 (ISBN)

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In Part 3 of the First Trilogy "Characterising Locally Finite Groups Satisfying the Strong Sylow Theorem for the Prime p" & "About the Strong Sylow Theorem for the Prime p in Simple Locally Finite Groups" & "The Strong Sylow Theorem for the Prime p in Projective Special Linear Locally Finite Groups" we continue the program begun in [10] to optimise along the way 1) its beautiful Theorem about the first type "An" of infinite families of finite simple groups step-by-step to further types by proving it for the second type "A = PSLn". We start with proving the beautiful Conjecture 2 of [10] about the General Linear Groups over (commutative) locally finite fields, stating that their rank is bounded in terms of their p-uniqueness, and then break down this insight to the Special Linear Groups and the Projective Special Linear (PSL) Groups over locally finite fields. We close with suggestions for future research -> regarding the remaining rank-unbounded types (the "Classical Groups") and the way 2), -> regarding the (locally) finite and p-soluble groups, and -> regarding Augustin-Louis Cauchy's and Évariste Galois' contributions to Sylow theory in finite groups, which culminate in the announcement of a Second Trilogy.

Felix F. Flemisch proudly received his first 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, UK, and finally his degree Dipl.-Math. at marvellous and fabulous Freiburg i.Br. in 1985. From February 1981 until April 1985 he was quite happily affiliated to the 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.

Erscheinungsdatum	19.09.2023
Reihe/Serie	Sylow Theory in Locally Finite Groups ; 3
Sprache	englisch
Maße	215 x 303 mm
Gewicht	437 g
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	conjugacy of maximal (= Sylow) p-subgroups • locally finite group satisfying the (strong) Sylow Theorem for the prime p • minimal p-unique subgroup • p-uniqueness subgroup • singular (Sylow) p-subgroup • (very) good Sylow p-subgroup
ISBN-13	9783757860011 / 9783757860011
Zustand	Neuware