First Trilogy about Sylow Theory in Locally Finite Groups Three manuscripts on Sylow theory in locally finite groups
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- Deutsch, Englisch, Französisch ausgewählt
119,99 €
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Beschreibung
Produktdetails
Einband
Gebundene Ausgabe
Erscheinungsdatum
15.11.2023
Abbildungen
264 Farbabb.
Verlag
BoD – Books on DemandSeitenzahl
264
Maße (L/B/H)
30,3/21,5/2,2 cm
Gewicht
1046 g
Auflage
2
Sprache
Deutsch, Englisch, Französisch
ISBN
978-3-7504-0398-7
The Second edition introduces a uniform page numbering, adds page numbers to the appendices, improves 19 pages, adds Pages 109 to 112 and a Table of Contents.
Part 2 (ISBN 978-3-7543-3642-8) of the Trilogy is based on the author's research paper "About the Strong Sylow Theorem for the Prime p in Simple Locally Finite Groups".
We first give an overview of simple locally finite groups and reduce their Sylow theory for the prime p to a conjecture of Prof. Otto H. Kegel about the rank-unbounded ones of the 19 known families of finite simple groups. Part 2 introduces a new scheme to describe the 19 families, the family T of types, defines the rank of each type, and emphasises the rôle of Kegel covers. This part presents a unified picture of known results and is the reason why our title starts with "About".
We then apply new ideas to prove the conjecture for the alternating groups (see Page ii).
Thereupon we remember Kegel covers and *-sequences. Finally we suggest a plan how to prove the conjecture step-by-step which leads to further conjectures thereby unifying Sylow theory in locally finite simple groups with Sylow theory in locally finite and p-soluble groups.
In Part 3 (ISBN 978-3-7578-6001-1) of the Trilogy we continue the program begun in [10] to optimise along the way 1) its 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 Conjecture 2 of [10] about the General Linear Groups by using new ideas (see Page ii), and then break down this insight to the Special Linear and the PSL Groups. We close with suggestions for future research regarding the remaining rank-unbounded types (the "Classical Groups") and the way 2), the (locally) finite and p-soluble groups, and Augustin-Louis Cauchy's and Évariste Galois' contributions to Sylow theory in finite groups.
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