Some results concerning a transformation semigroup

J. S. V. Symons

doi:10.1017/S1446788700034455

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The full transformation semigroup F(X) is extremely important. As far back as 1952, Malcev (1952) showed that its automorphism group consisted of mappings of the form g-1 · g, g ∈ G(X). The present work is devoted to a generalization of this result.

References

Clifford, A. H. and Preston, G. B. (1961, 1967), The algebraic theory of semigroups, Vols. I and II (Math. Surveys of the American Math. Soc., 7, 1961 and 1967).Google Scholar

Magill, K. D. Jr, (1966), ‘Subsemigroups of S(X)’, Math. Japon. 11, 109–115.Google Scholar

Malcev, A. I. (1952), ‘Symmetric groupoids’, Mat. Sb. (N. S.) 13 (73), 136–151.Google Scholar

Scott, W. R. (1964), Group Theory, (Prentice-Hall, 1964).Google Scholar

Sierpinski, W. (1958), Cardinal and Ordinal Numbers, (Warszawa, 1958).Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Nenthein, S. and Kemprasit, Y. 2006. On transformation semigroups which are ℬ𝒬‐semigroups. International Journal of Mathematics and Mathematical Sciences, Vol. 2006, Issue. 1,

Sanwong, Jintana Sommanee, Worachead and Redfield, Robert 2008. Regularity and Green′s Relations on a Semigroup ofTransformations with Restricted Range. International Journal of Mathematics and Mathematical Sciences, Vol. 2008, Issue. 1,

SULLIVAN, R. P. 2008. SEMIGROUPS OF LINEAR TRANSFORMATIONS WITH RESTRICTED RANGE. Bulletin of the Australian Mathematical Society, Vol. 77, Issue. 3, p. 441.

Sanwong, Jintana Singha, Boorapa and Sullivan, R. P. 2009. Maximal and minimal congruences on some semigroups. Acta Mathematica Sinica, English Series, Vol. 25, Issue. 3, p. 455.

MENDES-GONÇALVES, SUZANA and SULLIVAN, R. P. 2011. THE IDEAL STRUCTURE OF SEMIGROUPS OF TRANSFORMATIONS WITH RESTRICTED RANGE. Bulletin of the Australian Mathematical Society, Vol. 83, Issue. 2, p. 289.

Sanwong, Jintana 2011. The regular part of a semigroup of transformations with restricted range. Semigroup Forum, Vol. 83, Issue. 1, p. 134.

Honyam, Preeyanuch and Sanwong, Jintana 2011. SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET. Journal of the Korean Mathematical Society, Vol. 48, Issue. 2, p. 289.

Udomkavanich, Patanee and Jitjankarn, Phichet 2012. A classification of regressive transformation semigroups on chains. Semigroup Forum, Vol. 85, Issue. 3, p. 559.

SANGKHANAN, KRITSADA and SANWONG, JINTANA 2012. PARTIAL ORDERS ON SEMIGROUPS OF PARTIAL TRANSFORMATIONS WITH RESTRICTED RANGE. Bulletin of the Australian Mathematical Society, Vol. 86, Issue. 1, p. 100.

SUN, LEI and WANG, LIMIN 2013. NATURAL PARTIAL ORDER IN SEMIGROUPS OF TRANSFORMATIONS WITH INVARIANT SET. Bulletin of the Australian Mathematical Society, Vol. 87, Issue. 1, p. 94.

Sun, Lei 2013. A note on abundance of certain semigroups of transformations with restricted range. Semigroup Forum, Vol. 87, Issue. 3, p. 681.

Fernandes, Vítor H. Honyam, Preeyanuch Quinteiro, Teresa M. and Singha, Boorapa 2014. On semigroups of endomorphisms of a chain with restricted range. Semigroup Forum, Vol. 89, Issue. 1, p. 77.

Jitjankarn, Phichet and Rungratgasame, Thitarie 2015. A Note on Isomorphism Theorems for Semigroups of Order-Preserving Transformations with Restricted Range. International Journal of Mathematics and Mathematical Sciences, Vol. 2015, Issue. , p. 1.

Dolinka, Igor and East, James 2015. Variants of finite full transformation semigroups. International Journal of Algebra and Computation, Vol. 25, Issue. 08, p. 1187.

Sommanee, Worachead and Sanwong, Jintana 2015. Order-preserving transformations with restricted range: regularity, Green’s relations, and ideals. Algebra universalis, Vol. 74, Issue. 3-4, p. 277.

Fernandes, Vítor H. Honyam, Preeyanuch Quinteiro, Teresa M. and Singha, Boorapa 2016. On Semigroups of Orientation-preserving Transformations with Restricted Range. Communications in Algebra, Vol. 44, Issue. 1, p. 253.

Sun, Lei and Sun, Junling 2016. A natural partial order on certain semigroups of transformations with restricted range. Semigroup Forum, Vol. 92, Issue. 1, p. 135.

Tinpun, K. and Koppitz, J. 2016. Generating sets of infinite full transformation semigroups with restricted range. Acta Scientiarum Mathematicarum, Vol. 82, Issue. 1-2, p. 55.

SOMMANEE, WORACHEAD and SANGKHANAN, KRITSADA 2017. THE REGULAR PART OF A SEMIGROUP OF LINEAR TRANSFORMATIONS WITH RESTRICTED RANGE. Journal of the Australian Mathematical Society, Vol. 103, Issue. 3, p. 402.

Zhang, Jia and Luo, Yanfeng 2017. On certain order-preserving transformation semigroups. Communications in Algebra, Vol. 45, Issue. 7, p. 2980.

Download full list

Article contents

Some results concerning a transformation semigroup

Extract

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests