Geodesic
A Method for Constructing Square Roots in Finite Full Transformation Semigroups
Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 344-351

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Let Tn denote the full transformation semigroup on the set X = {1,2,. . .,n}, that is the set of all mappings from X to X, the semigroup operation being composition of mappings. The aim of this paper is to provide a method for the construction of all square roots of an arbitrary element α ∈ Tn, by employing a representation of the members of Tn as special directed graphs.
DOI : 10.4153/CMB-1986-053-2
Mots-clés : 20M20, 05C20 
Higgins, Peter M. A Method for Constructing Square Roots in Finite Full Transformation Semigroups. Canadian mathematical bulletin, Tome 29 (1986) no. 3, pp. 344-351. doi: 10.4153/CMB-1986-053-2
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     author = {Higgins, Peter M.},
     title = {A {Method} for {Constructing} {Square} {Roots} in {Finite} {Full} {Transformation} {Semigroups}},
     journal = {Canadian mathematical bulletin},
     pages = {344--351},
     year = {1986},
     volume = {29},
     number = {3},
     doi = {10.4153/CMB-1986-053-2},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1986-053-2/}
}
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