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math.GR2026
The Margolis-Rhodes Monoid of a Graph
Stuart Margolis, John Rhodes
We investigate the structural, combinatorial, ideal-theoretic and Krohn-Rhodes complexity of the Margolis-Rhodes monoid, MR(G), of a finite simple graph G, viewed topologically as…
math.GR2026
Aperiodic Flows on Finite Semigroups II: Smallish Monoids Suffice for Complexity 1
Stuart Margolis, John Rhodes
A smallish monoid M is a monoid that has a unique 0-minimal ideal I(M) that is a 0-simple subsemigroup and such that its regular J -classes are the group of units and the two in I(…
math.GR2026
Bases of Permutation Groups and Boolean Representable Simplicial Complexes
Stuart Margolis, John Rhodes
A base of a permutation group (X,G) is a subset B of X such that its pointwise stabilizer is the trivial group. A list (x1,x2, ... ,xk) of elements of X is irredundant if each elem…