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 - Hardcover

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

Buch. Zustand: Neu. Neuware -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.Books on Demand GmbH, Überseering 33, 22297 Hamburg 48 pp. Englisch. Artikel-Nr. 9783757860011

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