Regular semigroups generated by a group and a transformation
Let Tn and Sn be the full transformation semigroup and the symmetric group on Xn ={1,2,…,n},respectively.Suppose that K(n,r)={α∈Tn| rank(α)≤r},G≤Sn andα∈Tn\Sn.In this paper we mainly determine the equivalent characterizations between transitive groups corresponding to a class of regular transformation semigroups by GAP.The main content is as follows:1)When<G,α>is a regular semigroup for each transformation in K(n,n-2),we give the equivalent characterizations of transitive groups and their orders;2)When<G,α>is a regular semigroup for each transformation in K(n,3),we give the equivalent characterizations of transitive groups and their orders.
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