| Title:
|
A combinatorial property and power graphs of semigroups (English) |
| Author:
|
Kelarev, A. V. |
| Author:
|
Quinn, S. J. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
2004 |
| Pages:
|
1-7 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
sequences |
| Keyword:
|
power graphs |
| Keyword:
|
semigroups |
| MSC:
|
05C20 |
| MSC:
|
05C25 |
| MSC:
|
20M99 |
| idZBL:
|
Zbl 1099.05042 |
| idMR:
|
MR2076856 |
| . |
| Date available:
|
2009-05-05T16:42:56Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119433 |
| . |
| Reference:
|
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| Reference:
|
[2] Graham R.L.: Rudiments of Ramsey Theory.Amer. Math. Soc., Providence, R.I., 1981. Zbl 0555.05051, MR 0608630 |
| Reference:
|
[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. MR 1470003 |
| Reference:
|
[4] de Luca A., Varricchio S.: Finiteness and Regularity in Semigroups and Formal Languages.Monographs in Theoretical Computer Science, Springer, Berlin, 1998. Zbl 0935.68056 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[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. Zbl 0914.68155, MR 1647316 |
| Reference:
|
[8] Kelarev A.V.: Ring Constructions and Applications.World Scientific, 2002. Zbl 0999.16036, MR 1875643 |
| Reference:
|
[9] Kelarev A.V.: Graph Algebras and Automata.Marcel Dekker, 2003. Zbl 1070.68097, MR 2064147 |
| Reference:
|
[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. Zbl 0966.05040, MR 1777663 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| . |
