Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all finite subgroups of the orthogonal groups in two and three dimensions. The presentation is somewhat less formal than in succeeding chapters. For instance, the existence of the icosahedron is accepted as an empirical fact, and no formal proof of existence is included. Throughout most of Chapter 2 we do not distinguish between groups that are "geo- metrically indistinguishable," that is, conjugate in the orthogonal group. Very little of the...
Chapter 1 introduces some of the terminology and notation used later and indicates prerequisites. Chapter 2 gives a reasonably thorough account of all...
An authoritative, full-year course on both group theory and ordinary character theory--essential tools for mathematics and the physical sciences
One of the few treatments available combining both group theory and character theory, Groups and Characters is an effective general textbook on these two fundamentally connected subjects. Presuming only a basic knowledge of abstract algebra as in a first-year graduate course, the text opens with a review of background material and then guides readers carefully through several of the most important aspects of groups and characters,...
An authoritative, full-year course on both group theory and ordinary character theory--essential tools for mathematics and the physical sciences ...
This graduate-level text is intended for initial courses in algebra that begin with first principles but proceed at a faster pace than undergraduate-level courses. It employs presentations and proofs that are accessible to students, and it provides numerous concrete examples. Exercises appear throughout the text, clarifying concepts as they arise; additional exercises, varying widely in difficulty, are included at the ends of the chapters. Subjects include groups, rings, fields and Galois theory, modules, and structure of rings and algebras. Further topics encompass infinite Abelian...
This graduate-level text is intended for initial courses in algebra that begin with first principles but proceed at a faster pace than undergraduat...
