Word Problem for Groups and Monoids

[摘要] Chapter 1 defines basic ideas such as definition of monoids, homomorphisms of monoids, congruences, factor monoids, free monoids, monoid presentations (rewriting systems), homomorphisms of monoids defined by presentations into known monoids, equivalent rewriting system, Tietze transformation and noetherian induction. In chapter 2 we give definitions of some properties of rewriting systems, eg noetherian, confluency, locally confluency and completeness. We also mention some well known reduction orderings. Some important theorems and lemmas are proved, which will later be used in the thesis. We define what is meant by a monoid to be left (right) FPinfinity. In chapter 3 we constuct free groups, free product of two monoids, monoids with amalgamated submonoids, HNN-extension in monoids and finally monoids with commutative submonoids using the concept of monoid presentations (rewriting system). The irreducibles of each presentation is discussed. And in each presentation, we emphasize that the irreducibles are unique, using theorems and lemmas proved in chapter 2. The word problem for monoids and groups is discussed in chapter 4. Examples of groups and monoids with solvable (unsolvable) word problem are given. We discuss residual properties of a monoid (group) and prove that residually finite monoids have solvable word problem.

[发布机构] University:University of Glasgow

[关键词] Mathematics