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A smallest generating set of a semigroup is a generating set of the smallest cardinality. Similarly, an irredundant generating setX is a generating set such that no proper subset of X is also a generating set. A semigroup S is ubiquitous if every irredundant generating set of S is of the same cardinality. We are motivated by a naïve algorithm to find a small generating set for a semigroup, which in...
We find some perhaps surprising isomorphism results for the groups {Vn(G)}, where Vn(G) is a supergroup of the Higman–Thompson group Vn for n ∈ N and G ≤ Sn, the symmetric group on n points. These groups, introduced by Farley and Hughes, are the groups generated by Vn and the tree automorphisms [α]g defined as follows. For each g ∈ G and each node α in the infinite rooted n-ary tree, the automorphisms...
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