Abstract:Let Ω be a finite set and T (Ω) be the full transformation monoid on Ω. The rank of a transformation t ∈ T (Ω) is the natural number |Ωt|. Given A ⊆ T (Ω), denote by A the semigroup generated by A. Let k be a fixed natural number such that 2 ≤ k ≤ |Ω|. In the first part of this paper we (almost) classify the permutation groups G on Ω such that for all rank k transformation t ∈ T (Ω), every element in S t := G, t can be written as a product eg, where e 2 = e ∈ S t and g ∈ G. In the second part we prove, among o… Show more
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