Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groups
نویسندگان
چکیده
منابع مشابه
On One-relator Inverse Monoids and One-relator Groups
It is known that the word problem for one-relator groups and for one-relator monoids of the form Mon〈A ‖ w = 1〉 is decidable. However, the question of decidability of the word problem for general one-relation monoids of the form M = Mon〈A ‖ u = v〉 where u and v are arbitrary (positive) words in A remains open. The present paper is concerned with one-relator inverse monoids with a presentation o...
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Theorem 1 The word problem for any 1-relator monoids can be reduced to the left side divisibility problem for monoids M presented in 2 generators by 1 defining relation of the form aU = bV . For the solution of this problem it sufficies to find an algorithm to recognize for any word aW (or for any word bW ) whether or not it is left side divisible in M by the letter b (accordingly by the letter...
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Birget, J.-C., SW. Margolis and J.C. Meakin, The word problem for inverse monoids presented by one idempotent relator, Theoretical Computer Science 123 (1994) 2733289. We study inverse monoids presented by a finite set of generators and one relation e= I, where e is a word representing an idempotent in the free inverse monoid, and 1 is the empty word. We show that (1) the word problem is solvab...
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It is a well-known fact that every group G has a presentation of the form G = F/R, where F is a free group and R the kernel of the natural epimorphism from F onto G. Driven by the desire to obtain a similar presentation of the group of automorphisms Aut(G), we can consider the subgroup Stab(R) ⊆ Aut(F ) of those automorphisms of F that stabilize R, and try to figure out if the natural homomorph...
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ژورنال
عنوان ژورنال: Inventiones mathematicae
سال: 2019
ISSN: 0020-9910,1432-1297
DOI: 10.1007/s00222-019-00920-2