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}
}
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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.
