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A Method for Constructing Square Roots in Finite Full Transformation Semigroups

Published online by Cambridge University Press:  20 November 2018

Peter M. Higgins
Peter M. Higgins*
Affiliation:
California State University, Chico Chico, California95929
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Abstract

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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.

Keywords

20M2005C20
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 29 , Issue 3 , 01 September 1986 , pp. 344 - 351
Copyright
Copyright © Canadian Mathematical Society 1986

References

1. Harary, F., Graph Theory, Addison-Wesley, 1969.Google Scholar
2. Snowden, M. and Howie, J. M., Square roots infinite full transformation semigroups, Glasgow Math. J., 23(1982), pp. 137–149.Google Scholar