Combinatorial Algebra: Syntax and Semantics

Mark V. Sapir is a Centennial Professor of Mathematics at Vanderbilt University.

"This book concentrates on the following three topics: the Burnside problem, the finite basis property and growth of algebras. ... this book is a very valuable addition to the mathematical literature. ... shows that there are 'universal' methods which can be used to investigate many algebraic problems from different parts of algebra ... . it should also be noted that the book presents self-contained proofs of important recent results which were available only in research articles till now." (Konrad P. Pioro, Mathematical Reviews, July, 2015) "The book explores connections and interactions between 'semantics' (that is, 'objects' like graphs, topological spaces, etc.) and 'syntactics' (i.e. the means to speak about objects like words, laws, etc.) which occur in the analysis of algebraic structures. ... The book ... is addressed to active readers of a certain level of mathematical maturity. Included are more than 350 exercises and a collection of open problems." (K. Auinger, Monatshefte fur Mathematik, 2015) "The book should be viewed as an encyclopedia of algebraic facts which have strong combinatorial flavor both in their statement and in proofs. ... The book should be of interest to different audiences who want to be introduced to the fascinating world of combinatorial algebra, ranging from undergraduate students to senior scientists." (Vadim Gorin, zbMATH 1319.05001, 2015)

• Introduction.- 1. Main definitions and basic fact.- 2. Words that can be avoided.- 3. Semigroups.- 4. Rings.- 5. Groups.- Bibliography.- Index.