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We investigate the complexity of algorithmic problems on finitely generated subgroups of free groups. Margolis and Meakin showed how a finite monoid Synt(H) can be canonically and effectively associated with such a subgroup H. We show that H is pure (that is, closed under radical) if and only if Synt(H) is aperiodic. We also show that testing for this… (More)
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… (More)
RR esum e. On dd emontre que la conjecture forte de Hanna Neumann, sur le rang de l'intersection de sous-groupes de type ni d'un groupe libre, est vv eriii ee pour une large classe de sous-groupes, caractt eris es par des proprii et es gg eom etriques. Un cas particulier de notre rr esultat entra^ ne que la conjecture est vraie pour les sous-groupes de type… (More)
It is known that the problem of determining consistency of a finite system of equations in a free group or a free monoid is decidable, but the corresponding problem for systems of equations in a free inverse monoid of rank at least two is undecidable. Any solution to a system of equations in a free inverse monoid induces a solution to the corresponding… (More)
We develop some new topological tools to study maximal subgroups of free idempotent generated semigroups. As an application, we show that the rank 1 component of the free idempotent generated semigroup of the biordered set of a full matrix monoid of size n×n, n > 2 over a division ring Q has maximal subgroup isomorphic to the multi-plicative subgroup of Q.
1 2 1 2 1 2. U have the same set of idempotents , then the amalgam is strongly embeddable in a regular semigroup S that contains S , S , and U as full regular subsemigroups. In 1 2 this case the inductive structure of the amalgamated free produce S) S was 1 U 2 studied by Nambooripad and Pastijn in 1989, using Ordman's results from 1971 on amalgams of… (More)