A combinatorial property and power graphs of semigroups

Andrei V. Kelarev; Stephen J. Quinn

Commentationes Mathematicae Universitatis Carolinae (2004)

  • Volume: 45, Issue: 1, page 1-7
  • ISSN: 0010-2628

Abstract

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Research on combinatorial properties of sequences in groups and semigroups originates from Bernhard Neumann's theorem answering a question of Paul Erd"{o}s. For results on related combinatorial properties of sequences in semigroups we refer to the book [3]. In 2000 the authors introduced a new combinatorial property and described all groups satisfying it. The present paper extends this result to all semigroups.

How to cite

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Kelarev, Andrei V., and Quinn, Stephen J.. "A combinatorial property and power graphs of semigroups." Commentationes Mathematicae Universitatis Carolinae 45.1 (2004): 1-7. <http://eudml.org/doc/249330>.

@article{Kelarev2004,
abstract = {Research on combinatorial properties of sequences in groups and semigroups originates from Bernhard Neumann's theorem answering a question of Paul Erd"\{o\}s. For results on related combinatorial properties of sequences in semigroups we refer to the book [3]. In 2000 the authors introduced a new combinatorial property and described all groups satisfying it. The present paper extends this result to all semigroups.},
author = {Kelarev, Andrei V., Quinn, Stephen J.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {sequences; power graphs; semigroups},
language = {eng},
number = {1},
pages = {1-7},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {A combinatorial property and power graphs of semigroups},
url = {http://eudml.org/doc/249330},
volume = {45},
year = {2004},
}

TY - JOUR
AU - Kelarev, Andrei V.
AU - Quinn, Stephen J.
TI - A combinatorial property and power graphs of semigroups
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2004
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 45
IS - 1
SP - 1
EP - 7
AB - Research on combinatorial properties of sequences in groups and semigroups originates from Bernhard Neumann's theorem answering a question of Paul Erd"{o}s. For results on related combinatorial properties of sequences in semigroups we refer to the book [3]. In 2000 the authors introduced a new combinatorial property and described all groups satisfying it. The present paper extends this result to all semigroups.
LA - eng
KW - sequences; power graphs; semigroups
UR - http://eudml.org/doc/249330
ER -

References

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  1. Chartland G., Lesniak L., Graphs and Digraphs, Chapman & Hall, London, 1996. MR1408678
  2. Graham R.L., Rudiments of Ramsey Theory, Amer. Math. Soc., Providence, R.I., 1981. Zbl0555.05051MR0608630
  3. de Luca A., Varricchio S., Regularity and finiteness conditions, Handbook of Formal Languages, Vol. 1, Eds. G. Rosenberg, A. Salomaa, Springer-Verlag, Berlin, 1997, 747-810. MR1470003
  4. de Luca A., Varricchio S., Finiteness and Regularity in Semigroups and Formal Languages, Monographs in Theoretical Computer Science, Springer, Berlin, 1998. Zbl0935.68056
  5. Howie J.M., Fundamentals of Semigroup Theory, Clarendon Press, Oxford, 1995. Zbl0835.20077MR1455373
  6. Justin J., Pirillo G., On some questions and conjectures in combinatorial semigroup theory, Southeast Asian Bull. Math. 18 (1994), 91-104. (1994) MR1319315
  7. Kelarev A.V., Combinatorial properties of sequences in groups and semigroups, {Combinatorics, Complexity and Logic}, Eds. D.S. Bridge, C.S. Calude, J. Gibbons, S. Reeves, I.H. Witten, (Springer Ser. Discrete Math. Theor. Comput. Soc.), Springer-Verlag, Singapore, 1997, pp289-2983. Zbl0914.68155MR1647316
  8. Kelarev A.V., Ring Constructions and Applications, World Scientific, 2002. Zbl0999.16036MR1875643
  9. Kelarev A.V., Graph Algebras and Automata, Marcel Dekker, 2003. Zbl1070.68097MR2064147
  10. Kelarev A.V., Quinn S.J., A combinatorial property and power graphs of groups, Contrib. General Algebra 12, 58. Arbeitstagung Allgemeine Algebra (Vienna University of Technology, June 3-6, 1999) Eds. D. Dorninger, G. Eigenthaler, M. Goldstern, H.K. Kaiser, W. More, W.B. Mueller, Springer-Verlag, 2000, pp.229-235. Zbl0966.05040MR1777663
  11. Kelarev A.V., Quinn S.J., A combinatorial property of Cayley graphs and semigroups, Semigroup Forum 66 (2003), 89-96. (2003) MR1939667
  12. Kelarev A.V., Quinn S.J., Directed graphs and combinatorial properties of semigroups, J. Algebra 251 (2002), 1 16-26. (2002) Zbl1005.20043MR1900273
  13. Kelarev A.V., Quinn S.J., Power graphs and semigroups of matrices, Bull. Austral. Math. Soc. 63 (2001), 341-344. (2001) Zbl1043.20042MR1823720
  14. Lothair M., Combinatorics on Words, Addison-Wesley, Tokyo, 1982. MR0675953
  15. Neumann B.H., A problem of Paul Erdös on groups, J. Austral. Math. Soc. 21 (1976), 467-472. (1976) Zbl0333.05110MR0419283
  16. Pin J.-E., Syntactic semigroups, Handbook of Formal Languages. Vol. 1. Word, Language, Grammar. Eds. G. Rozenberg, A. Salomaa, Springer-Verlag, Berlin, 1997, pp.679-746. MR1470002
  17. Robinson D.J.S., A Course in the Theory of Groups, Springer, New-York, Berlin, 1982. Zbl0836.20001MR0648604
  18. Shevrin L.N., Ovsyannikov A.J., Semigroups and their Subsemigroup Lattices, Kluwer, Dordrecht, 1996. Zbl0858.20054MR1420413

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