Download or read book Groups which Contain an Abelian Subgroup of Prime Index written by George Abram Miller and published by . This book was released on 1913 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Groups of Prime Power Order Volume 2 written by Yakov Berkovich and published by Walter de Gruyter. This book was released on 2008-12-10 with total page 613 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of three volumes devoted to elementary finite p-group theory. Similar to the first volume, hundreds of important results are analyzed and, in many cases, simplified. Important topics presented in this monograph include: (a) classification of p-groups all of whose cyclic subgroups of composite orders are normal, (b) classification of 2-groups with exactly three involutions, (c) two proofs of Ward's theorem on quaternion-free groups, (d) 2-groups with small centralizers of an involution, (e) classification of 2-groups with exactly four cyclic subgroups of order 2n > 2, (f) two new proofs of Blackburn's theorem on minimal nonmetacyclic groups, (g) classification of p-groups all of whose subgroups of index p2 are abelian, (h) classification of 2-groups all of whose minimal nonabelian subgroups have order 8, (i) p-groups with cyclic subgroups of index p2 are classified. This volume contains hundreds of original exercises (with all difficult exercises being solved) and an extended list of about 700 open problems. The book is based on Volume 1, and it is suitable for researchers and graduate students of mathematics with a modest background on algebra.
Download or read book Groups of Prime Power Order Volume 1 written by Yakov Berkovich and published by Walter de Gruyter. This book was released on 2008-12-10 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first of three volumes of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this monograph include: (a) counting of subgroups, with almost all main counting theorems being proved, (b) regular p-groups and regularity criteria, (c) p-groups of maximal class and their numerous characterizations, (d) characters of p-groups, (e) p-groups with large Schur multiplier and commutator subgroups, (f) (p‒1)-admissible Hall chains in normal subgroups, (g) powerful p-groups, (h) automorphisms of p-groups, (i) p-groups all of whose nonnormal subgroups are cyclic, (j) Alperin's problem on abelian subgroups of small index. The book is suitable for researchers and graduate students of mathematics with a modest background on algebra. It also contains hundreds of original exercises (with difficult exercises being solved) and a comprehensive list of about 700 open problems.
Download or read book Groups of Prime Power Order Volume 5 written by Yakov G. Berkovich and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-01-15 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fifth volume of a comprehensive and elementary treatment of finite p-group theory. Topics covered in this volume include theory of linear algebras and Lie algebras. 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 Groups of Prime Power Order written by I︠A︡. G. Berkovich and published by de Gruyter. This book was released on 2008 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: Main description: This is the first of three volumes on finite p-group theory. It presents the state of the art and in addition contains numerous new and easy proofs of famous theorems, many exercises (some of them with solutions), and about 1500 open problems. It is expected to be useful to certain applied mathematics areas, such as combinatorics, coding theory, and computer sciences. The book should also be easily comprehensible to students and scientists with some basic knowledge of group theory and algebra.
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 Finite Permutation Groups written by Helmut Wielandt and published by Academic Press. This book was released on 2014-05-10 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Permutation Groups provides an introduction to the basic facts of both the theory of abstract finite groups and the theory of permutation groups. This book deals with older theorems on multiply transitive groups as well as on simply transitive groups. Organized into five chapters, this book begins with an overview of the fundamental concepts of notation and Frobenius group. This text then discusses the modifications of multiple transitivity and can be used to deduce an improved form of the classical theorem. Other chapters consider the concept of simply transitive permutation groups. This book discusses as well permutation groups in the framework of representation theory. The final chapter deals with Frobenius' theory of group characters. This book is a valuable resource for engineers, mathematicians, and research workers. Graduate students and readers who are interested in finite permutation groups will also find this book useful.
Download or read book Ranks of Groups written by Martyn R. Dixon and published by John Wiley & Sons. This book was released on 2017-06-15 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to ranks and group theory Ranks of Groups features a logical, straightforward presentation, beginning with a succinct discussion of the standard ranks before moving on to specific aspects of ranks of groups. Topics covered include section ranks, groups of finite 0-rank, minimax rank, special rank, groups of finite section p-rank, groups having finite section p-rank for all primes p, groups of finite bounded section rank, groups whose abelian subgroups have finite rank, groups whose abelian subgroups have bounded finite rank, finitely generated groups having finite rank, residual properties of groups of finite rank, groups covered by normal subgroups of bounded finite rank, and theorems of Schur and Baer. This book presents fundamental concepts and notions related to the area of ranks in groups. Class-tested worldwide by highly qualified authors in the fields of abstract algebra and group theory, this book focuses on critical concepts with the most interesting, striking, and central results. In order to provide readers with the most useful techniques related to the various different ranks in a group, the authors have carefully examined hundreds of current research articles on group theory authored by researchers around the world, providing an up-to-date, comprehensive treatment of the subject. • All material has been thoroughly vetted and class-tested by well-known researchers who have worked in the area of rank conditions in groups • Topical coverage reflects the most modern, up-to-date research on ranks of groups • Features a unified point-of-view on the most important results in ranks obtained using various methods so as to illustrate the role those ranks play within group theory • Focuses on the tools and methods concerning ranks necessary to achieve significant progress in the study and clarification of the structure of groups Ranks of Groups: The Tools, Characteristics, and Restrictions is an excellent textbook for graduate courses in mathematics, featuring numerous exercises, whose solutions are provided. This book will be an indispensable resource for mathematicians and researchers specializing in group theory and abstract algebra. MARTYN R. DIXON, PhD, is Professor in the Department of Mathematics at the University of Alabama. LEONID A. KURDACHENKO, PhD, DrS, is Distinguished Professor and Chair of the Department of Algebra at the University of Dnepropetrovsk, Ukraine. IGOR YA SUBBOTIN, PhD, is Professor in the Department of Mathematics and Natural Sciences at National University in Los Angeles, California.
Download or read book An Introduction to the Theory of Groups of Finite Order written by Harold Hilton and published by . This book was released on 1908 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Groups of Prime Power Order Volume 6 written by Yakov G. Berkovich and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-06-25 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the sixth volume of a comprehensive and elementary treatment of finite group theory. This volume contains many hundreds of original exercises (including solutions for the more difficult ones) and an extended list of about 1000 open problems. The current book is based on Volumes 1–5 and it is suitable for researchers and graduate students working in group theory.
Download or read book Groups of Prime Power Order Volume 4 written by Yakov G. Berkovich and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-12-14 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fourth volume of a comprehensive and elementary treatment of finite p-group theory. As in the previous volumes, minimal nonabelian p-groups play an important role. Topics covered in this volume include: subgroup structure of metacyclic p-groups Ishikawa’s theorem on p-groups with two sizes of conjugate classes p-central p-groups theorem of Kegel on nilpotence of H p-groups partitions of p-groups characterizations of Dedekindian groups norm of p-groups p-groups with 2-uniserial subgroups of small order The book also contains hundreds of original exercises and solutions and a comprehensive list of more than 500 open problems. This work is suitable for researchers and graduate students with a modest background in algebra.
Download or read book Annals of Mathematics written by and published by . This book was released on 1912 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Classification of the Finite Simple Groups Number 3 written by Daniel Gorenstein and published by American Mathematical Soc.. This book was released on 1994 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines the internal structure of the finite simple groups of Lie type, the finite alternating groups, and 26 sporadic finite simple groups, as well as their analogues. Emphasis is on the structure of local subgroups and their relationships with one another, rather than development of an abstract theory of simple groups. A foundation is laid for the development of specific properties of K-groups to be used in the inductive proof of the classification theorem. Highlights include statements and proofs of the Breol-Tits and Curtis-Tits theorems, and material on centralizers of semisimple involutions in groups of Lie type. For graduate students and research mathematicians. Annotation copyrighted by Book News, Inc., Portland, OR
Download or read book Proceedings of the National Academy of Sciences of the United States of America written by and published by . This book was released on 1944 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Bulletin of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1922 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Transactions of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1907 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: Monthly journal devoted entirely to research in pure and applied mathematics, and, in general, includes longer papers than those in the Proceedings of the American Mathematical Society.
Download or read book American Journal of Mathematics written by and published by . This book was released on 1928 with total page 668 pages. Available in PDF, EPUB and Kindle. Book excerpt: The American Journal of Mathematics publishes research papers and articles of broad appeal covering the major areas of contemporary mathematics.
