John C. Meakin

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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(More)
w x T. E. Hall proved in 1978 that if S , S ; U is an amalgam of regular semigroups 1 2 Ž in which S l S s U is a full regular subsemigroup of S and S i.e., S , S , and 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(More)
Let S be a semigroup with set E(S) of idempotents, and let 〈E(S)〉 denote the subsemigroup of S generated by E(S). We say that S is an idempotent generated semigroup if S = 〈E(S)〉. Idempotent generated semigroups have received considerable attention in the literature. For example, an early result of J. A. Erdös [7] proves that the idempotent generated part(More)
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)
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 multiplicative subgroup of Q.
The notion of upper distortion for graded submonoids embedded in groups and monoids is introduced. A finitely generated monoid M is graded if every element of M can be written in only finitely many ways in terms of some fixed system of generators. Examples of such monoids are free monoids, Artin monoids, and monoids satisfying certain small cancellation(More)