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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)
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)