Groups St Andrews 2005: Volume 1

Groups St Andrews 2005: Volume 1

Author: C. M. Campbell

Publisher: Cambridge University Press

Published: 2007-01-04

Total Pages: 463

ISBN-13: 0521694698

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Selected papers from 'Groups St Andrews 2005' cover a wide spectrum of modern group theory.


Ischia Group Theory 2010

Ischia Group Theory 2010

Author: Mariagrazia Bianchi

Publisher: World Scientific

Published: 2012

Total Pages: 416

ISBN-13: 9814350052

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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


Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras

Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras

Author: Martin W. Liebeck

Publisher: American Mathematical Soc.

Published: 2012-01-25

Total Pages: 394

ISBN-13: 0821869205

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This book concerns the theory of unipotent elements in simple algebraic groups over algebraically closed or finite fields, and nilpotent elements in the corresponding simple Lie algebras. These topics have been an important area of study for decades, with applications to representation theory, character theory, the subgroup structure of algebraic groups and finite groups, and the classification of the finite simple groups. The main focus is on obtaining full information on class representatives and centralizers of unipotent and nilpotent elements. Although there is a substantial literature on this topic, this book is the first single source where such information is presented completely in all characteristics. In addition, many of the results are new--for example, those concerning centralizers of nilpotent elements in small characteristics. Indeed, the whole approach, while using some ideas from the literature, is novel, and yields many new general and specific facts concerning the structure and embeddings of centralizers.


Handbook of Algebra

Handbook of Algebra

Author: M. Hazewinkel

Publisher: Elsevier

Published: 2008-04-18

Total Pages: 577

ISBN-13: 0080569412

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Algebra, as we know it today, consists of many different ideas, concepts and results. A reasonable estimate of the number of these different items would be somewhere between 50,000 and 200,000. Many of these have been named and many more could (and perhaps should) have a name or a convenient designation. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. If this happens, one should be able to find enough information in this Handbook to judge if it is worthwhile to pursue the quest. In addition to the primary information given in the Handbook, there are references to relevant articles, books or lecture notes to help the reader. An excellent index has been included which is extensive and not limited to definitions, theorems etc. The Handbook of Algebra will publish articles as they are received and thus the reader will find in this third volume articles from twelve different sections. The advantages of this scheme are two-fold: accepted articles will be published quickly and the outline of the Handbook can be allowed to evolve as the various volumes are published. A particularly important function of the Handbook is to provide professional mathematicians working in an area other than their own with sufficient information on the topic in question if and when it is needed. - Thorough and practical source of information - Provides in-depth coverage of new topics in algebra - Includes references to relevant articles, books and lecture notes


Hopf Algebras and Galois Module Theory

Hopf Algebras and Galois Module Theory

Author: Lindsay N. Childs

Publisher: American Mathematical Soc.

Published: 2021-11-10

Total Pages: 311

ISBN-13: 1470465167

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Hopf algebras have been shown to play a natural role in studying questions of integral module structure in extensions of local or global fields. This book surveys the state of the art in Hopf-Galois theory and Hopf-Galois module theory and can be viewed as a sequel to the first author's book, Taming Wild Extensions: Hopf Algebras and Local Galois Module Theory, which was published in 2000. The book is divided into two parts. Part I is more algebraic and focuses on Hopf-Galois structures on Galois field extensions, as well as the connection between this topic and the theory of skew braces. Part II is more number theoretical and studies the application of Hopf algebras to questions of integral module structure in extensions of local or global fields. Graduate students and researchers with a general background in graduate-level algebra, algebraic number theory, and some familiarity with Hopf algebras will appreciate the overview of the current state of this exciting area and the suggestions for numerous avenues for further research and investigation.


Lower Central and Dimension Series of Groups

Lower Central and Dimension Series of Groups

Author: Roman Mikhailov

Publisher: Springer Science & Business Media

Published: 2009

Total Pages: 367

ISBN-13: 3540858172

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A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series is a challenging task. This monograph presents an exposition of different methods for investigating this relationship.