On the Extension Problem for Partial Permutations
نویسندگان
چکیده
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, and P do not preserve decidability. In addition, several joins, including A ∨U, are shown to be undecidable.
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