Download or read book A Study of Fixed point free Automorphisms and Solvable Groups written by Emanuel Psaras and published by . This book was released on 2020 with total page 65 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1903, Ferdinand Georg Frobenius made a conjecture that can be stated as such: let G be a group that emits a fixed-point-free automorphism. Then, G is a solvable group. Throughout the rest of the 20th century many different specific cases of this conjecture have been proved (with the cases putting a restriction on the order of the automorphism). For example, in 1959 John Thompson proved this for all such automorphisms with prime order. Later on in the 70's, Elizabeth Ralston proved this result for autmorphisms with the order being a product of two distinct primes for two primes. Finally in the 90's the full conjecture was accepted as being proven as a consequence of some results in the landmark Classification of Finite Simple Groups. As a result, an attempt at an all-encompassing and unified proof of this conjecture has been largely abandoned by group theorists. For this thesis, we will look at a specific case of this conjecture where the order of the automorphism is 4 (as also done in [5]) and try to give a formal proof whilst introducing the necessary results used as tools in said proof.

Download or read book Finite Groups with Fixed point free Automorphisms of Prime Order written by John Thompson and published by . This book was released on 1959 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Solvability of Finite Groups Admitting Fixed point free Automorphisms of Order Rs written by Elizabeth Wall Ralston and published by . This book was released on 1970 with total page 92 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite Groups with Fixed point free Automorphisms of Prime Order written by John Thompson and published by . This book was released on 1959 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Finite Groups Admitting a Fixed point free Automorphism written by Peter J. Rowley and published by . This book was released on 2020 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Nilpotent Groups and their Automorphisms written by Evgenii I. Khukhro and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 269 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany

Download or read book On generalized fixed point free automorphisms of finite groups written by and published by . This book was released on 1999 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Self contained Review of Thompson s Fixed point free Automorphism Theorem written by Mario F. Sracic and published by . This book was released on 2014 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the early 1900s, Frobenius conjectured if a group [italic G] admits a fixed-point-free automorphism [italic Phi], then [italic G] must be solvable. During the next half-century, mathematicians would struggle to find a completely group theoretic proof of Frobenius' Conjecture. Between 1960 and 1980, progress was made on the Conjecture only by assuming conditions on the order of [italic Phi]. In 1959, Thompson proved, for his dissertation, the case assuming the automorphism had prime order and resulted in a stronger condition than solvable [Tho59]; Hernstein and Gorenstein proved the conjecture with an automorphism of order 4 [DG61]; and in 1972, Ralston proved a group admitting a fixed-point-free automorphism with order [italic pq] is solvable, where [italic p] and [italic q] are primes. [Ral72] It was not until the 1980s, with the power of the Classification of Finite Simple Groups, was Frobenius' Conjecture finally proven; however, the proof involved character theory. In this paper, we consider John Thompson's case of the Frobenius Conjecture: Theorem ([Tho59]). Let G be a group admitting a fixed-point-free automorphism of prime order. Then G is nilpotent. Our goal is to lay a complete framework of the necessary concepts and theorems leading up to, and including, the proof of Thompson's theorem.

Download or read book On Finite Groups Admitting a Fixed point free Automorphism Goup written by Martin Ross Pettet and published by . This book was released on 1974 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Solubility of Finite Groups Admitting a Certain Fixed point free Group of Automorphisms written by John Doyle (D.Phil.) and published by . This book was released on 1986 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Groups Admitting a Fixed point free Group of Automorphisms Isomorphic to S3 written by Barry E. Dolman and published by . This book was released on 1983 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Groups St Andrews 2001 in Oxford Volume 2 written by C. M. Campbell and published by Cambridge University Press. This book was released on 2003-11-06 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of the two-volume book contains selected papers from the conference 'Groups St Andrews 2001 in Oxford'. The articles are contributed by a number of leading researchers and cover a wide spectrum of modern group theory. There are articles based on lecture courses given by five main speakers together with refereed survey and research articles. The 'Groups St Andrews' proceedings volumes are a snapshot of the state of the art in group theory and they often play an important role in future developments in the subject.

Download or read book Finite Fixed Point Free Automorphism Groups written by Peter Mayr and published by . This book was released on 1998 with total page 84 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Santa Cruz Conference on Finite Groups written by Bruce Cooperstein and published by American Mathematical Soc.. This book was released on 1980 with total page 654 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book P Automorphisms of Finite P Groups written by Evgenii I. Khukhro and published by Cambridge University Press. This book was released on 1998-02-13 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers working in group theory and Lie rings.

Download or read book Ischia Group Theory 2010 written by Mariagrazia Bianchi and published by World Scientific. This book was released on 2012 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Download or read book Issues in General and Specialized Mathematics Research 2013 Edition written by and published by ScholarlyEditions. This book was released on 2013-05-01 with total page 1919 pages. Available in PDF, EPUB and Kindle. Book excerpt: Issues in General and Specialized Mathematics Research: 2013 Edition is a ScholarlyEditions™ book that delivers timely, authoritative, and comprehensive information about General Mathematics. The editors have built Issues in General and Specialized Mathematics Research: 2013 Edition on the vast information databases of ScholarlyNews.™ You can expect the information about General Mathematics in this book to be deeper than what you can access anywhere else, as well as consistently reliable, authoritative, informed, and relevant. The content of Issues in General and Specialized Mathematics Research: 2013 Edition has been produced by the world’s leading scientists, engineers, analysts, research institutions, and companies. All of the content is from peer-reviewed sources, and all of it is written, assembled, and edited by the editors at ScholarlyEditions™ and available exclusively from us. You now have a source you can cite with authority, confidence, and credibility. More information is available at http://www.ScholarlyEditions.com/.