Download or read book The Maximum Order Finite Groups of Outer Automorphisms of Free Groups written by Sicheng Wang and published by . This book was released on 1993 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Automorphisms of Finite Groups written by Inder Bir Singh Passi and published by Springer. This book was released on 2019-01-12 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.
Download or read book Surface realizable Finite Groups of Outer Automorphisms of Finitely generated Free Groups written by Christopher Thomas and published by . This book was released on 2001 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: A homeomorphism from a punctured surface to itself induces an outer automorphism of the free fundamental group of the surface, an outer automorphism which can be called surface-realizable. This paper provides necessary and sufficient conditions for a finite abelian group of outer automorphisms of a finitely-generated free group to be surface-realizable. Furthermore, n.a.s.c. are given for any finite group of such outer automorphisms to be realized by orientation-preserving homeomorphisms of an orientable surface. These properties are identified by examining those finite subgroups of automorphisms which are mapped into the group of outer automorphisms by the usual projection, and making sure that the non-trivial automorphisms fix either a trivial or cyclic subgroup of the free group. Examples are given to show the difficulties in applying this method to non-abelian cases.
Download or read book Finite Groups of Outer Automorphisms of Free Groups of Finite Rank written by Yuxing Wang and published by . This book was released on 1996 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Atlas of Finite Groups written by John Horton Conway and published by Oxford University Press. This book was released on 1985 with total page 252 pages. Available in PDF, EPUB and Kindle. Book excerpt: This atlas covers groups from the families of the classification of finite simple groups. Recently updated incorporating corrections
Download or read book Automorphisms of Finite Groups written by Inder Bir S. Passi and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.--
Download or read book Geometric Group Theory written by Mladen Bestvina and published by American Mathematical Soc.. This book was released on 2014-12-24 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geometric group theory refers to the study of discrete groups using tools from topology, geometry, dynamics and analysis. The field is evolving very rapidly and the present volume provides an introduction to and overview of various topics which have played critical roles in this evolution. The book contains lecture notes from courses given at the Park City Math Institute on Geometric Group Theory. The institute consists of a set of intensive short courses offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The courses begin at an introductory level suitable for graduate students and lead up to currently active topics of research. The articles in this volume include introductions to CAT(0) cube complexes and groups, to modern small cancellation theory, to isometry groups of general CAT(0) spaces, and a discussion of nilpotent genus in the context of mapping class groups and CAT(0) groups. One course surveys quasi-isometric rigidity, others contain an exploration of the geometry of Outer space, of actions of arithmetic groups, lectures on lattices and locally symmetric spaces, on marked length spectra and on expander graphs, Property tau and approximate groups. This book is a valuable resource for graduate students and researchers interested in geometric group theory. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Download or read book The Maximal Factorizations of the Finite Simple Groups and Their Automorphism Groups written by Martin W. Liebeck and published by American Mathematical Soc.. This book was released on 1990 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main result describes completely the maximal factorizations of all the finite simple groups and their automorphism groups. As a consequence, a classification of the maximal subgroups of the finite alternating and symmetric groups is obtained.
Download or read book Finite Groups written by Daniel Gorenstein and published by American Mathematical Soc.. This book was released on 2007 with total page 546 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The Classification Theorem is one of the main achievements of 20th century mathematics, but its proof has not yet been completely extricated from the journal literature in which it first appeared. This is the second volume in a series devoted to the presentation of a reorganized and simplified proof of the classification of the finite simple groups. The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series. This volume provides a relatively concise and readable access to the key ideas and theorems underlying the study of finite simple groups and their important subgroups. The sections on semisimple subgroups and subgroups of parabolic type give detailed treatments of these important subgroups, including some results not available until now or available only in journal literature. The signalizer section provides an extensive development of both the Bender Method and the Signalizer Functor Method, which play a central role in the proof of the Classification Theorem. This book would be a valuable companion text for a graduate group theory course."--Publisher's website
Download or read book A Survey of Knot Theory written by Akio Kawauchi and published by Birkhäuser. This book was released on 2012-12-06 with total page 431 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knot theory is a rapidly developing field of research with many applications, not only for mathematics. The present volume, written by a well-known specialist, gives a complete survey of this theory from its very beginnings to today's most recent research results. An indispensable book for everyone concerned with knot theory.
Download or read book Some Solvable Subgroups of the Outer Automorphism Group of a Finite Group written by Nguyen Cao Dam and published by . This book was released on 1972 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Centralizers of Finite Subgroups of Automorphisms and Outer Automorphisms of Free Groups written by Debra Lynn Boutin and published by . This book was released on 1998 with total page 146 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Groups Admitting Fixed Point Free Automorphisms of Order Pq written by K.-N. Cheng and published by . This book was released on 1985 with total page 10 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Groups of Prime Power Order Volume 3 written by Yakov Berkovich and published by Walter de Gruyter. This book was released on 2011-06-30 with total page 669 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the third volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume: impact of minimal nonabelian subgroups on the structure of p-groups, classification of groups all of whose nonnormal subgroups have the same order, degrees of irreducible characters of p-groups associated with finite algebras, groups covered by few proper subgroups, p-groups of element breadth 2 and subgroup breadth 1, exact number of subgroups of given order in a metacyclic p-group, soft subgroups, p-groups with a maximal elementary abelian subgroup of order p2, p-groups generated by certain minimal nonabelian subgroups, p-groups in which certain nonabelian subgroups are 2-generator. The book contains many dozens of original exercises (with difficult exercises being solved) and a list of about 900 research problems and themes.
Download or read book On Finite Groups Admitting a Fixed point free Automorphism of Order 2n written by Voon-Ka Lim and published by . This book was released on 1980 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Some Finite Groups Admitting on Automorphism of Order Two written by Voon-Ka Lim and published by . This book was released on 1984 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Finite Groups of Automorphisms written by Norman Biggs and published by CUP Archive. This book was released on 1971-10-31 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: These are notes of lectures given at the University of Southampton, October-December 1969. The lectures were intended for research students working in areas related to the topics discussed, and for mathematicians working in other fields who were interested in hearing a survey of some current problems and their background. The character of the lectures has been retained by the inclusion of occasional 'philosophical' remarks, but the text has been kept free of references as far as possible.
