## The Uniform Word Problem for Groups and Finite Rees Quotients of E-Unitary Inverse Semigroups (2001)

Citations: | 2 - 1 self |

### BibTeX

@MISC{Steinberg01theuniform,

author = {Benjamin Steinberg},

title = {The Uniform Word Problem for Groups and Finite Rees Quotients of E-Unitary Inverse Semigroups},

year = {2001}

}

### OpenURL

### Abstract

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 nite 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 nite labeled graph in the Cayley graph of a group in C. This latter problem is shown to be equivalent to deciding whether a nite labeled graph is a Schutzenberger graph of an E-unitary inverse semigroup with maximal group image in C. 1.