Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groups

2019/02/28 by Robert D. Gray · 1 citation
Mathematics · #math.GR #msc:20F10 #msc:20F05 #msc:20M05 #msc:20M18 #msc:20F36

paper · pdf · doi:10.1007/s00222-019-00920-2

19 pages; updated version with minor changes

arxiv created 2019/03/18 · arxiv updated 2020/02/19

Abstract

We prove the following results: (1) There is a one-relator inverse monoid Inv⟨ A | w=1 ⟩ 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.

Cited by

• The word problem for two-generator one-relator inverse monoids