Model Theory of Groups and Automorphism Groups

Model Theory of Groups and Automorphism Groups
Author: David M. Evans
Publisher: Cambridge University Press
Total Pages: 232
Release: 1997-07-10
Genre: Mathematics
ISBN: 052158955X

Surveys recent interactions between model theory and other branches of mathematics, notably group theory.

Advances in Algebra and Model Theory

Advances in Algebra and Model Theory
Author: M Droste
Publisher: CRC Press
Total Pages: 516
Release: 1998-01-29
Genre: Mathematics
ISBN: 9789056991012

Contains 25 surveys in algebra and model theory, all written by leading experts in the field. The surveys are based around talks given at conferences held in Essen, 1994, and Dresden, 1995. Each contribution is written in such a way as to highlight the ideas that were discussed at the conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community. The topics include field and ring theory as well as groups, ordered algebraic structure and their relationship to model theory. Several papers deal with infinite permutation groups, abelian groups, modules and their relatives and representations. Model theoretic aspects include quantifier elimination in skew fields, Hilbert's 17th problem, (aleph-0)-categorical structures and Boolean algebras. Moreover symmetry questions and automorphism groups of orders are covered. This work contains 25 surveys in algebra and model theory, each is written in such a way as to highlight the ideas that were discussed at Conferences, and also to stimulate open research problems in a form accessible to the whole mathematical community.

Tits Buildings and the Model Theory of Groups

Tits Buildings and the Model Theory of Groups
Author: Katrin Tent
Publisher: Cambridge University Press
Total Pages: 314
Release: 2002-01-03
Genre: Mathematics
ISBN: 9780521010634

Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.

Finite Group Theory

Finite Group Theory
Author: I. Martin Isaacs
Publisher: American Mathematical Society
Total Pages: 368
Release: 2023-01-24
Genre: Mathematics
ISBN: 1470471604

The text begins with a review of group actions and Sylow theory. It includes semidirect products, the Schur–Zassenhaus theorem, the theory of commutators, coprime actions on groups, transfer theory, Frobenius groups, primitive and multiply transitive permutation groups, the simplicity of the PSL groups, the generalized Fitting subgroup and also Thompson's J-subgroup and his normal $p$-complement theorem. Topics that seldom (or never) appear in books are also covered. These include subnormality theory, a group-theoretic proof of Burnside's theorem about groups with order divisible by just two primes, the Wielandt automorphism tower theorem, Yoshida's transfer theorem, the “principal ideal theorem” of transfer theory and many smaller results that are not very well known. Proofs often contain original ideas, and they are given in complete detail. In many cases they are simpler than can be found elsewhere. The book is largely based on the author's lectures, and consequently, the style is friendly and somewhat informal. Finally, the book includes a large collection of problems at disparate levels of difficulty. These should enable students to practice group theory and not just read about it. Martin Isaacs is professor of mathematics at the University of Wisconsin, Madison. Over the years, he has received many teaching awards and is well known for his inspiring teaching and lecturing. He received the University of Wisconsin Distinguished Teaching Award in 1985, the Benjamin Smith Reynolds Teaching Award in 1989, and the Wisconsin Section MAA Teaching Award in 1993, to name only a few. He was also honored by being the selected MAA Pólya Lecturer in 2003–2005.

Model Theory : An Introduction

Model Theory : An Introduction
Author: David Marker
Publisher: Springer Science & Business Media
Total Pages: 342
Release: 2006-04-06
Genre: Mathematics
ISBN: 0387227342

Assumes only a familiarity with algebra at the beginning graduate level; Stresses applications to algebra; Illustrates several of the ways Model Theory can be a useful tool in analyzing classical mathematical structures

Groups, Combinatorics and Geometry

Groups, Combinatorics and Geometry
Author: Martin W. Liebeck
Publisher: Cambridge University Press
Total Pages: 505
Release: 1992-09-10
Genre: Mathematics
ISBN: 0521406854

This volume contains a collection of papers on the subject of the classification of finite simple groups.

A Course in Model Theory

A Course in Model Theory
Author: Katrin Tent
Publisher: Cambridge University Press
Total Pages: 259
Release: 2012-03-08
Genre: Mathematics
ISBN: 052176324X

Concise introduction to current topics in model theory, including simple and stable theories.

A Course in the Theory of Groups

A Course in the Theory of Groups
Author: Derek J.S. Robinson
Publisher: Springer Science & Business Media
Total Pages: 498
Release: 2012-12-06
Genre: Mathematics
ISBN: 1468401289

" A group is defined by means of the laws of combinations of its symbols," according to a celebrated dictum of Cayley. And this is probably still as good a one-line explanation as any. The concept of a group is surely one of the central ideas of mathematics. Certainly there are a few branches of that science in which groups are not employed implicitly or explicitly. Nor is the use of groups confined to pure mathematics. Quantum theory, molecular and atomic structure, and crystallography are just a few of the areas of science in which the idea of a group as a measure of symmetry has played an important part. The theory of groups is the oldest branch of modern algebra. Its origins are to be found in the work of Joseph Louis Lagrange (1736-1813), Paulo Ruffini (1765-1822), and Evariste Galois (1811-1832) on the theory of algebraic equations. Their groups consisted of permutations of the variables or of the roots of polynomials, and indeed for much of the nineteenth century all groups were finite permutation groups. Nevertheless many of the fundamental ideas of group theory were introduced by these early workers and their successors, Augustin Louis Cauchy (1789-1857), Ludwig Sylow (1832-1918), Camille Jordan (1838-1922) among others. The concept of an abstract group is clearly recognizable in the work of Arthur Cayley (1821-1895) but it did not really win widespread acceptance until Walther von Dyck (1856-1934) introduced presentations of groups.

Groups and Model Theory

Groups and Model Theory
Author: Lutz Strungmann
Publisher: American Mathematical Soc.
Total Pages: 336
Release: 2012
Genre: Mathematics
ISBN: 082186923X

Contains the proceedings of the conference Groups and Model Theory, held 2011, in Ruhr, Germany. Articles cover abelian groups, modules over commutative rings, permutation groups, automorphism groups of homogeneous structures such as graphs, relational structures, geometries, topological spaces or groups, consequences of model theoretic properties like stability or categoricity, subgroups of small index, the automorphism tower problem, as well as random constructions.