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9 papers · 1 filter
Quasi-isometry and finite presentations of left cancellative monoids
Robert D. Gray, Mark Kambites
We show that being finitely presentable and being finitely presentable with solvable word problem are quasi-isometry invariants of finitely generated left cancellative monoids. Our…
Uniform decision problems and abstract properties of small overlap monoids
Mark Kambites
We study the way in which the abstract structure of a small overlap monoid is reflected in, and may be algorithmically deduced from, a small overlap presentation. We show that ever…
A note on the definition of small overlap monoids
Mark Kambites
Small overlap conditions are simple and natural combinatorial conditions on semigroup and monoid presentations, which serve to limit the complexity of derivation sequences between…
Multiplicative structure of 2x2 tropical matrices
Marianne Johnson, Mark Kambites
We study the algebraic structure of the semigroup of all tropical matrices under multiplication. Using ideas from tropical geometry, we give a complete description of…
Groups acting on semimetric spaces and quasi-isometries of monoids
Robert Gray, Mark Kambites
We study groups acting by length-preserving transformations on spaces equipped with asymmetric, partially-defined distance functions. We introduce a natural notion of quasi-isometr…
Weyl groups of small groups of finite Morley rank
Jeffrey Burdges, Adrien Deloro
We examine Weyl groups of minimal connected simple groups of finite Morley rank of degenerate type. We show that they are cyclic, and lift isomorphically to subgroups of the ambien…