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Author: Martyn Russell Dixon Publisher: World Scientific ISBN: 9789810217952 Category : Mathematics Languages : en Pages : 324
Book Description
This book is concerned with the generalizations of Sylow theorems and the related topics of formations and the fitting of classes to locally finite groups. It also contains details of Sunkov's and Belyaev'ss results on locally finite groups with min-p for all primes p. This is the first time many of these topics have appeared in book form. The body of work here is fairly complete.
Author: Martyn Russell Dixon Publisher: World Scientific ISBN: 9789810217952 Category : Mathematics Languages : en Pages : 324
Book Description
This book is concerned with the generalizations of Sylow theorems and the related topics of formations and the fitting of classes to locally finite groups. It also contains details of Sunkov's and Belyaev'ss results on locally finite groups with min-p for all primes p. This is the first time many of these topics have appeared in book form. The body of work here is fairly complete.
Author: Dipl.-Math. Felix Flemisch Publisher: BoD – Books on Demand ISBN: 3756234169 Category : Mathematics Languages : en Pages : 46
Book Description
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.
Author: Felix F. Flemisch Publisher: BoD – Books on Demand ISBN: 3756808017 Category : Mathematics Languages : en Pages : 122
Book Description
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].
Author: Dipl.-Math. Felix Flemisch Publisher: BoD – Books on Demand ISBN: 3754360876 Category : Mathematics Languages : en Pages : 118
Book Description
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.
Author: Dipl.-Math. Felix F. Flemisch Publisher: BoD – Books on Demand ISBN: 3758333202 Category : Mathematics Languages : en Pages : 69
Book Description
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.
Author: Dipl.-Math. Felix Flemisch Publisher: BoD – Books on Demand ISBN: 3756838927 Category : Mathematics Languages : en Pages : 26
Book Description
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].
Author: Martyn R. Dixon Publisher: CRC Press ISBN: 1000848310 Category : Mathematics Languages : en Pages : 411
Book Description
In recent times, group theory has found wider applications in various fields of algebra and mathematics in general. But in order to apply this or that result, you need to know about it, and such results are often diffuse and difficult to locate, necessitating that readers construct an extended search through multiple monographs, articles, and papers. Such readers must wade through the morass of concepts and auxiliary statements that are needed to understand the desired results, while it is initially unclear which of them are really needed and which ones can be dispensed with. A further difficulty that one may encounter might be concerned with the form or language in which a given result is presented. For example, if someone knows the basics of group theory, but does not know the theory of representations, and a group theoretical result is formulated in the language of representation theory, then that person is faced with the problem of translating this result into the language with which they are familiar, etc. Infinite Groups: A Roadmap to Some Classical Areas seeks to overcome this challenge. The book covers a broad swath of the theory of infinite groups, without giving proofs, but with all the concepts and auxiliary results necessary for understanding such results. In other words, this book is an extended directory, or a guide, to some of the more established areas of infinite groups. Features An excellent resource for a subject formerly lacking an accessible and in-depth reference Suitable for graduate students, PhD students, and researchers working in group theory Introduces the reader to the most important methods, ideas, approaches, and constructions in infinite group theory.
Author: C. M. Campbell Publisher: Cambridge University Press ISBN: 9781139437219 Category : Mathematics Languages : en Pages : 316
Book Description
This first volume of the two-volume book contains selected papers from the international conference 'Groups St Andrews 2001 in Oxford' which was held at the University of Oxford in August 2001. Five main lecture courses were given at the conference, and articles based on their lectures form a substantial part of the Proceedings. This volume contains the contributions from Marston Conder (Auckland), Persi Diaconis (Stanford) and Marcus Du Sautoy (Cambridge). The series of Proceedings of Groups St Andrews conferences have provided snapshots of the state of research in group theory throughout the past twenty years. As with earlier volumes, these refereed volumes also contain accessible surveys of contemporary research fronts, as well as a diverse collection of short research articles. They form a valuable reference for researchers, especially graduate students, working in group theory.
Author: Mariagrazia Bianchi Publisher: World Scientific ISBN: 9814350052 Category : Mathematics Languages : en Pages : 416
Book Description
Positive laws on generators in powerful pro-p groups / C. Acciarri and G.A. Fernandez-Alcober -- Periodic groups saturated by dihedral subgroups / B. Amberg and L. Kazarin -- A note on finite groups in which the conjugacy class sizes form an arithmetic progression / M. Bianchi, A. Gillio and P.P. Palfy -- A survey of recent progress on non-abelian tensor squares of groups / R.D. Blyth, F. Fumagalli and M. Morigi -- Conjugacy classes of subgroups of finite p-groups: the first gap / R. Brandl -- The Tutte polynomial of the Schreier graphs of the Grigorchuck group and the Basilica group / T. Ceccherini-Silberstein, A. Donno and D. Iacono -- On maximal subgroups of the alternating and symmetric groups / V. Colombo -- Markov's problems through the looking glass of Zariski and Markov topologies / D. Dikranjan and D. Toller -- Linear groups with finite dimensional orbits / M.R. Dixon, L.A. Kurdachenko and J. Otal -- Three-dimensional loops as sections in a four-dimensional solvable Lie group / A. Figula -- A note on finite p-groups with a maximal elementary subgroup of rank 2 / G. Glauberman -- Finitely generated free by C[symbol] pro-p groups / W. Herfort and P.A. Zalesskii -- Finite nonabelian 2-groups all of whose minimal nonabelian subgroups are isomorphic to M[symbol] / Z. Janko -- Twisted conjugacy in certain Artin groups / A. Juhasz -- Applications of Clifford's theorem to Frobenius groups of automorphisms / E.I. Khukhro -- Inducing [symbol]-partial characters with a given vertex / M.L. Lewis -- Groups and Lie rings with Frobenius groups of automorphisms / N. Yu. Makarenko -- On integral representations of finite groups / D. Malinin -- On p-groups of small powerful class / A. Mann -- Lifting (2, k)-generators of linear groups / A. Maroti and C. Tamburini Bellani -- Fixed point subgroups and character tables / G. Navarro -- Permutability and seriality in locally finite groups / D.J.S. Robinson -- On the exponent of a finite group with a four-group of automorphisms / E. Romano and P. Shumyatsky -- Examples of Markov chains on spaces with multiplicities / F. Scarabotti and F. Tolli -- On the order and the element orders of finite groups: results and problems / W.J. Shi -- On local finiteness of verbal subgroups in residually finite groups / P. Shumyatsky -- The adjoint group of radical rings and related questions / Ya. P. Sysak -- On the Gorenstein dimension of soluble groups / O. Talelli -- Decomposition numbers for projective modules of finite Chevalley groups / A.E. Zalesski
Author: Martyn Russell Dixon
Author: Martyn Russell Dixon
Author: Dipl.-Math. Felix Flemisch
Author: Felix F. Flemisch
Author: Dipl.-Math. Felix Flemisch
Author: Dipl.-Math. Felix F. Flemisch
Author: Dipl.-Math. Felix Flemisch
Author: Martyn R. Dixon
Author: C. M. Campbell
Author: C. M. Campbell
Author: Mariagrazia Bianchi