The Strong Sylow Theorem For The Prime P In Simple Locally Finite Groups
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About The Strong Sylow Theorem For The Prime P In Simple Locally Finite Groups Part 2 Of A Trilogy
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Author : Dipl.-Math. Felix Flemisch
language : en
Publisher: BoD – Books on Demand
Release Date : 2023-03-30
About The Strong Sylow Theorem For The Prime P In Simple Locally Finite Groups Part 2 Of A Trilogy written by Dipl.-Math. Felix Flemisch and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-30 with Mathematics categories.
Part 2 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" is based on the author's research paper "About the Strong Sylow Theorem for the Prime p in Simple Locally Finite Groups". This very beautiful and pioneering manuscript had been submitted for peer reviewing to the open access journals Advances in Group Theory and Applications (AGTA) (see https://www.advgrouptheory.com/journal/) and Science Research Association (SCIREA) Journal of Mathematics (see https://www.scirea.org/journal/Mathematics) but was very regrettably rejected by both of them (with ridiculous arguments). We first give a profound overview of the structure of simple groups and in particular of the simple locally finite groups and reduce their Sylow theory for the prime p to a famous conjecture of Prof. Otto H. Kegel (see [16], Theorem 2.4: "Let the p-subgroup P be a p-uniqueness subgroup in the finite simple group S which belongs to one of the seven rank-unbounded families. Then the rank of S is bounded in terms of P.") 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 all proofs of which are by reference and it is the actual reason why our title starts with "About". We then apply beautiful new ideas to prove the conjecture for the alternating groups (see Page ii). Thereupon we are remembering Kegel covers and *-sequences. Finally we suggest a plan how to prove and even how to optimise the conjecture step-by-step or peu à peu which leads to further quite tough conjectures thereby unifying Sylow theory in locally finite simple groups with Sylow theory in locally finite and p-soluble groups. For any unexplained terminology we refer to [6].
The Strong Sylow Theorem For The Prime P In Simple Locally Finite Groups
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Author : Dipl.-Math. Felix F. Flemisch
language : en
Publisher: BoD – Books on Demand
Release Date : 2024-02-26
The Strong Sylow Theorem For The Prime P In Simple Locally Finite Groups written by Dipl.-Math. Felix F. Flemisch and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-26 with Mathematics categories.
This research paper continues [15]. We begin with giving a profound overview of the structure of arbitrary simple groups and in particular of the simple locally finite groups and reduce their Sylow theory for the prime p to a quite famous conjecture by Prof. Otto H. Kegel (see [37], Theorem 2.4: "Let the p-subgroup P be a p-uniqueness subgroup in the finite simple group S which belongs to one of the seven rank-unbounded families. Then the rank of S is bounded in terms of P.") about the rank-unbounded ones of the 19 known families of finite simple groups. We introduce a new scheme to describe the 19 families, the family T of types, define the rank of each type, and emphasise the rôle of Kegel covers. This part presents a unified picture of known results whose proofs are by reference. Subsequently we apply new ideas to prove the conjecture for the alternating groups. Thereupon we are remembering Kegel covers and *-sequences. Next we suggest a way 1) and a way 2) how to prove and even how to optimise Kegel's conjecture step-by-step or peu à peu which leads to Conjecture 1, Conjecture 2 and Conjecture 3 thereby unifying Sylow theory in locally finite simple groups with Sylow theory in locally finite and p-soluble groups whose joint study directs Sylow theory in (locally) finite groups. For any unexplained terminology we refer to [15]. We then continue the program begun above to optimise along the way 1) the 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 Conjecture 2 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 (locally) finite and p-soluble groups, and -> regarding Cauchy's and Galois' contributions to Sylow theory in finite groups. We much hope to enthuse group theorists with them. We include the predecessor research paper [15] as an Appendix.
The Strong Sylow Theorem For The Prime P In Projective Special Linear Locally Finite Groups Part 3 Of A Trilogy
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Author : Dipl.-Math. Felix F. Flemisch
language : en
Publisher: BoD – Books on Demand
Release Date : 2023-03-30
The Strong Sylow Theorem For The Prime P In Projective Special Linear Locally Finite Groups Part 3 Of A Trilogy written by Dipl.-Math. Felix F. Flemisch and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-30 with Mathematics categories.
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.
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P Part 1 Of A Trilogy
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Author : Dipl.-Math. Felix Flemisch
language : en
Publisher: BoD – Books on Demand
Release Date : 2023-03-07
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P Part 1 Of A Trilogy written by Dipl.-Math. Felix Flemisch and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-07 with Mathematics categories.
Part 1 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" is based on the beauteous BoD-Book "Characterising locally finite groups satisfying the strong Sylow Theorem for the prime p - Revised edition" (see ISBN 978-3-7562-3416-5) which in turn has been based on the author's research paper "Characterising Locally Finite Groups Satisfying the Strong Sylow Theorem for the Prime p" that was published on pp. 13-39 of Volume 13 of the gratifyingly open access mathematical journal Advances in Group Theory and Applications (AGTA) (see https://www.advgrouptheory.com/ journal/#read). Part 1 removes the highlights in light green of the Revised edition and adds the albeit considerably improved Pages i to vi, Pages 26a to 26f, and Pages xiii to xviii to the AGTA paper. In addition it adds the ten new Pages xv to xxiv to the Revised edition and thus renumbers the Pages xv to xviii into the Pages xxv to xxviii. It includes Reference [11] as Appendix 1 and Reference [10] as Appendix 2. Finally it calls to mind Prof. Otto H. Kegel's fine contribution to the conference Ischia Group Theory 2016.
The Strong Sylow Theorem For The Prime P In Projective Special Linear Locally Finite Groups Part 3 Of A Trilogy
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Author : Dipl.-Math. Felix F. Flemisch
language : en
Publisher: BoD – Books on Demand
Release Date : 2023-11-27
The Strong Sylow Theorem For The Prime P In Projective Special Linear Locally Finite Groups Part 3 Of A Trilogy written by Dipl.-Math. Felix F. Flemisch and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-27 with Mathematics categories.
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.
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P Part 1 Of A Trilogy
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Author : Felix F. Flemisch
language : en
Publisher: BoD – Books on Demand
Release Date : 2023-11-15
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P Part 1 Of A Trilogy written by Felix F. Flemisch and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-15 with Mathematics categories.
Part 1 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" is based on the beauteous BoD-Book "Characterising locally finite groups satisfying the strong Sylow Theorem for the prime p - Revised edition" (see ISBN 978-3-7562-3416-5) which in turn has been based on the author's research paper "Characterising Locally Finite Groups Satisfying the Strong Sylow Theorem for the Prime p" that was published on pp. 13-39 of Volume 13 of the open access mathematical journal Advances in Group Theory and Applications (AGTA) (look at https://www.advgrouptheory.com/journal/#read). The First edition of Part 1 (see ISBN 978-3-7543-6087-3) removes the highlights in light green of the Revised edition and adds the albeit fairly considerably improved Pages i to vi and Pages 27 to 34 to the AGTA paper. In addition Part 1 adds the ten new Pages 35 to 44 to the Revised edition and therefore has to renumber the Pages xv to xviii into the Pages 45 to 48. It includes the Reference [11] as Appendix 1 and the Reference [10] as Appendix 2. Finally it calls to mind Professor Otto H. Kegel's fine contribution to the conference Ischia Group Theory 2016. The Second edition introduces a uniform page numbering, adds page numbers to the appendices, improves Pages iv and v, Page 22, Pages 26 to 34 and Pages 39, 45, 49, 50, 75, 76, 105 and 106, adds Pages 109 to 112, and adds a two-page Table of Contents of the Trilogy. For a review of the trilogy see [16].
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P
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Author : Felix F. Flemisch
language : en
Publisher: BoD – Books on Demand
Release Date : 2021-10-05
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P written by Felix F. Flemisch and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-05 with Mathematics categories.
This publication presents the most essential portions of the author's German Diplomarbeit of 1984 and a "sprinkling" of new considerations and results as well which earnestly try to propose coming directions for (timeless and eternal) Sylow theory in (locally) finite groups. The 2nd edition provides quite a number of clarifications and corrections and adds the Chapter "Endnotes" which describes new proofs of historic relevance for the theorems of Lagrange and Cauchy on finite groups.
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P
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Author : Dipl.-Math. Felix Flemisch
language : en
Publisher: BoD – Books on Demand
Release Date : 2022-08-08
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P written by Dipl.-Math. Felix Flemisch and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-08-08 with Mathematics categories.
The Revised edition is based on the author's paper "Characterising Locally Finite Groups Satisfying the Strong Sylow Theorem for the Prime p" which has been published on pp. 13-39 of Volume 13 of the very fine open access mathematical journal Advances in Group Theory and Applications (AGTA) (see https://www.advgrouptheory.com/journal/#read). For that paper the author has transferred the copyright to AGTA. The Revised edition introduces quite a number of corrections and embellishments, highlighted in light green, which could not have been considered by AGTA, and especially a much more beautiful line and page formatting. For these enhancements the author has kept the copyright. The Revised edition adds Pages i to vi, Pages 26a to 26f and Pages xiii to xviii to the AGTA paper which either are required for a book - the front matter (die "Titelei") - or describe related aspects and background which cannot be published in a mathematical journal. The Revised edition incorporates major revisions by the author and by editors as well as some supplementary material designed to bring the research paper up to date.
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P
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Author : Felix F. Flemisch
language : en
Publisher: BoD – Books on Demand
Release Date : 2021-11-22
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P written by Felix F. Flemisch and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.
This publication presents the most essential portions of the author's German Diplomarbeit of 1984 and a "sprinkling" of new considerations and results as well which earnestly try to propose coming directions for the (timeless and eternal) Sylow theory in (locally) finite groups (see the pages 14, 15, 24 and xi to xxi). The line numbering provided facilitates and shall lively encourage (Scholarly Peer) Review. This edition proudly completes the Endnote g of the 3rd edition without line numbering (ISBN 978-3-7543-3213-9) with all the classical proofs and provides Appendix 1 and Appendix 2 for easy look at [1] and [8].
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P
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Author : Felix F. Flemisch
language : en
Publisher: BoD – Books on Demand
Release Date : 2021-10-25
Characterising Locally Finite Groups Satisfying The Strong Sylow Theorem For The Prime P written by Felix F. Flemisch and has been published by BoD – Books on Demand this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-25 with Mathematics categories.
This publication presents the most essential portions of the author's German Diplomarbeit of 1984 [2] and a "sprinkling" of some new considerations and results as well which earnestly try to propose coming directions for the (timeless and eternal) Sylow theory in (locally) finite groups (see the pages 14, 15, 20 and 24 to 34). The Mathematics edition extracts from the Full edition (see ISBN 978-3-7568-0801-4) all the very beautiful mathematical content. The Line numbering is facilitating and shall lively encourage (Scholarly Peer) Review. The First update considered comments by the author and an unknown referee. The Second update considers improvements of the Second edition of the Full edition and of the First Trilogy (see ISBN 978-3-7504-0398-7).