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

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

Buch | Spiralbindung

46 Seiten

2023 | 5. Auflage
BoD – Books on Demand (Verlag)
978-3-7568-9853-4 (ISBN)

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In Part 3 of the 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 = PSL n". We start with proving the 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 five 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.

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 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	13.01.2023
Reihe/Serie	Sylow Theory in Locally Finite Groups ; 3
Sprache	englisch
Maße	216 x 297 mm
Gewicht	144 g
Themenwelt	Mathematik / Informatik ► Mathematik
Schlagworte	algebraic closure of the prime field in characteristic p • ap, the numerical Sylow p-invariant p-uniqueness • complete reducibility • general linear group • G-isomorphic G-modules • G-module over a field F • Group of Lie type • Irreducibility • Jordan normal form • Kegel cover • locally finite field F • minimal p-unique subgroup • modular G-module • non-modular G-module • P-invariant Sylow p-subgroup • projective special linear group • PSL Group • p-uniqueness subgroup • rank of a locally finite simple group • Special linear group • strong Sylow Theorem for the prime p • twisted Chevalley group
ISBN-10	3-7568-9853-9 / 3756898539
ISBN-13	978-3-7568-9853-4 / 9783756898534
Zustand	Neuware