Robert D. Gray
Published 2019-02-11Version 1
We prove the following results: (1) There is a one-relator inverse monoid $\mathrm{Inv}\langle A\:|\:w=1 \rangle$ with undecidable word problem; and (2) There are one-relator groups with undecidable submonoid membership problem. The first of these results answers a problem originally posed by Margolis, Meakin and Stephen in 1987.
On groups of units of special and one-relator inverse monoids
L^2-Betti numbers of one-relator groups
Membership problems for positive one-relator groups and one-relation monoids
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