The uniform word problem for groups and finite Rees quotients of E-unitary inverse semigroups
✍ Scribed by Benjamin Steinberg
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 133 KB
- Volume
- 266
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
If C is a class of groups closed under taking subgroups, we show that the decidability of the uniform word problem for C is implied by the decidability of the membership problem for the class of finite Rees quotients of E-unitary inverse semigroups with maximal group image in C. The converse is shown if C is a pseudovariety.
When C is a pseudovariety, the above problems are shown to be equivalent to the problem of embedding a finite labeled graph in the Cayley graph of a group in C. This latter problem is shown to be equivalent to deciding whether a finite labeled graph is a Schützenberger graph of an E-unitary inverse semigroup with maximal group image in C.