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![The Strong Sylow Theorem for the Prime p in Projective Special Linear Locally Finite Groups - Part 3 of a Trilogy](https://images.bod.com/images/the-strong-sylow-theorem-for-the-prime-p-in-projective-special-linear-locally-finite-groups-part-3-of-a-trilogy-dipl-math-felix-f-flemisch-9783757860011.jpg/500/500/The_Strong_Sylow_Theorem_for_the_Prime_p_in_Projective_Special_Linear_Locally_Finite_Groups_-_Part_3_of_a_Trilogy.webp)
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
Band 3: Sylow Theory in Locally Finite Groups
Hardcover
48 Seiten
ISBN-13: 9783757860011
Verlag: Books on Demand
Erscheinungsdatum: 27.11.2023
Sprache: Englisch
44,99 €
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Mehr InfosIn 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.
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