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Varieties of Groups
Varieties of algebras are equationally defined classes of algebras, or "primitive classes" in MAL'CEV'S terminology. They made their first explicit appearance in the 1930's, in Garrett BIRKHOFF'S paper on "The structure of abstract algebras" and B. H. NEUMANN'S paper "Identical relations in groups I". For quite some time after this, there is little published evidence that the subject remained alive. In fact, however, as part of "universal algebra", it aroused great interest amongst those who had access, directly or indirectly, to PHILIP HALL'S lectures given at Cambridge late in the 1940's. More recently, category theory has provided a general setting since varieties, suitably interpreted, a...
Combinatorial Group Theory
This seminal, much-cited account begins with a fairly elementary exposition of basic concepts and a discussion of factor groups and subgroups. The topics of Nielsen transformations, free and amalgamated products, and commutator calculus receive detailed treatment. The concluding chapter surveys word, conjugacy, and related problems; adjunction and embedding problems; and more. Second, revised 1976 edition.
Combinatorial Group Theory
From the reviews: "This book [...] defines the boundaries of the subject now called combinatorial group theory. [...] it is a considerable achievement to have concentrated a survey of the subject into 339 pages. [...] a valuable and welcome addition to the literature, containing many results not previously available in a book. It will undoubtedly become a standard reference." Mathematical Reviews
Infinite Groups
In recent times, group theory has found wider applications in various fields of algebra and mathematics in general. But in order to apply this or that result, you need to know about it, and such results are often diffuse and difficult to locate, necessitating that readers construct an extended search through multiple monographs, articles, and papers. Such readers must wade through the morass of concepts and auxiliary statements that are needed to understand the desired results, while it is initially unclear which of them are really needed and which ones can be dispensed with. A further difficulty that one may encounter might be concerned with the form or language in which a given result is p...
The History of Combinatorial Group Theory
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 independ...
Groups of Prime Power Order
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.
Provability, Computability and Reflection
Provability, Computability and Reflection
