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Author: Roman Mikhailov
Publisher: Springer Science & Business Media
ISBN: 3540858172
Category : Mathematics
Languages : en
Pages : 367
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Book Description
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.
Author: Roman Mikhailov
Publisher: Springer Science & Business Media
ISBN: 3540858172
Category : Mathematics
Languages : en
Pages : 367
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Book Description
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.
Author: William Abikoff
Publisher: American Mathematical Soc.
ISBN: 082185156X
Category : Mathematics
Languages : en
Pages : 512
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Book Description
Wilhelm Magnus was an extraordinarily creative mathematician who made fundamental contributions to diverse areas, including group theory, geometry and special functions. This book contains the proceedings of a conference held in May 1992 at Polytechnic University, Brooklyn to honour the memory of Magnus. The focus of the book is on active areas of research where Magnus' influence can be seen. The papers range from expository articles to major new research, bringing together seemingly diverse topics and providing entry points to a variety of areas of mathematics.
Author: Lee Paul Neuwirth
Publisher: Princeton University Press
ISBN: 140088151X
Category : Mathematics
Languages : en
Pages : 352
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Book Description
There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields. These papers are dedicated to the memory of Ralph H. Fox, one of the world's leading topologists, by colleagues, former students, and friends. In knot theory, papers have been contributed by Goldsmith, Levine, Lomonaco, Perko, Trotter, and Whitten. Of these several are devoted to the study of branched covering spaces over knots and links, while others utilize the braid groups of Artin. Cossey and Smythe, Stallings, and Strasser address themselves to group theory. In his contribution Stallings describes the calculation of the groups In/In+1 where I is the augmentation ideal in a group ring RG. As a consequence, one has for each k an example of a k-generator l-relator group with no free homomorphs. In the third part, papers by Birman, Cappell, Milnor, Montesinos, Papakyriakopoulos, and Shalen comprise the treatment of 3-manifolds. Milnor gives, besides important new results, an exposition of certain aspects of our current knowledge regarding the 3- dimensional Brieskorn manifolds.
Author: S. Chmutov
Publisher: Cambridge University Press
ISBN: 1107020832
Category : Mathematics
Languages : en
Pages : 521
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Book Description
A detailed exposition of the theory with an emphasis on its combinatorial aspects.
Author: I.B.S. Passi
Publisher: Springer
ISBN: 354035297X
Category : Mathematics
Languages : en
Pages : 144
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Book Description
Author: Michael D. Atkinson
Publisher: Cambridge University Press
ISBN: 9780521788892
Category : Mathematics
Languages : en
Pages : 290
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Book Description
A collection of papers from leading researchers in algebra and geometric group theory.
Author: B. Chandler
Publisher: Springer Science & Business Media
ISBN: 1461394872
Category : Mathematics
Languages : en
Pages : 240
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Book Description
One of the pervasive phenomena in the history of science is the development of independent disciplines from the solution or attempted solutions of problems in other areas of science. In the Twentieth Century, the creation of specialties witqin the sciences has accelerated to the point where a large number of scientists in any major branch of science cannot understand the work of a colleague in another subdiscipline of his own science. Despite this fragmentation, the development of techniques or solutions of problems in one area very often contribute fundamentally to solutions of problems in a seemingly unrelated field. Therefore, an examination of this phenomenon of the formation of independent disciplines within the sciences would contrib ute to the understanding of their evolution in modern times. We believe that in this context the history of combinatorial group theory in the late Nineteenth Century and the Twentieth Century can be used effectively as a case study. It is a reasonably well-defined independent specialty, and yet it is closely related to other mathematical disciplines. The fact that combinatorial group theory has, so far, not been influenced by the practical needs of science and technology makes it possible for us to use combinatorial group theory to exhibit the role of the intellectual aspects of the development of mathematics in a clearcut manner. There are other features of combinatorial group theory which appear to make it a reasona ble choice as the object of a historical study.
Author: Matthias Aschenbrenner
Publisher: American Mathematical Soc.
ISBN: 0821888013
Category : Mathematics
Languages : en
Pages : 114
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Book Description
Given a prime , a group is called residually if the intersection of its -power index normal subgroups is trivial. A group is called virtually residually if it has a finite index subgroup which is residually . It is well-known that finitely generated linear groups over fields of characteristic zero are virtually residually for all but finitely many . In particular, fundamental groups of hyperbolic -manifolds are virtually residually . It is also well-known that fundamental groups of -manifolds are residually finite. In this paper the authors prove a common generalization of these results: every -manifold group is virtually residually for all but finitely many . This gives evidence for the conjecture (Thurston) that fundamental groups of -manifolds are linear groups.
Author: C. M. Campbell
Publisher: Cambridge University Press
ISBN: 9780521398497
Category : Mathematics
Languages : en
Pages : 268
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Book Description
Selected papers presented at the international conference on group theory held at St. Andrews in 1989 are combined in two volumes. The themes of the conference were combinatorial and computational group theory.
Author: Inder Bir Singh Passi
Publisher: Springer
ISBN: 9811328951
Category : Mathematics
Languages : en
Pages : 231
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Book Description
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.
