## On the extension problem for partial permutations (2003)

Venue: | PROC. AMER. MATH. SOC |

Citations: | 10 - 1 self |

### BibTeX

@ARTICLE{Auinger03onthe,

author = {K. Auinger and B. Steinberg},

title = {On the extension problem for partial permutations},

journal = {PROC. AMER. MATH. SOC},

year = {2003},

volume = {131},

number = {9},

pages = {2693--2703}

}

### OpenURL

### Abstract

A family of pseudovarieties of solvable groups is constructed, each of which has decidable membership and undecidable extension problem for partial permutations. Included are a pseudovariety U satisfying no non-trivial group identity and a metabelian pseudovariety Q. For each of these pseudovarieties V, the inverse monoid pseudovariety Sl∗V has undecidable membership problem. As a consequence, it is proved that the pseudovariety operators ∗, ∗∗, m○, ♦, ♦n, andP do not preserve decidability. In addition, several joins, including A ∨ U, are shown to be undecidable.