| Title:
|
Second centralizers of partial transformations (English) |
| Author:
|
Konieczny, Janusz |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
51 |
| Issue:
|
4 |
| Year:
|
2001 |
| Pages:
|
873-888 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Second centralizers of partial transformations on a finite set are determined. In particular, it is shown that the second centralizer of any partial transformation $\alpha $ consists of partial transformations that are locally powers of $\alpha $. (English) |
| Keyword:
|
partial transformation |
| Keyword:
|
second centralizer |
| MSC:
|
20M20 |
| idZBL:
|
Zbl 1003.20053 |
| idMR:
|
MR1864048 |
| . |
| Date available:
|
2009-09-24T10:47:59Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127692 |
| . |
| Reference:
|
[1] P. M. Higgins: Techniques of Semigroup Theory.Oxford University Press, New York, 1992. Zbl 0744.20046, MR 1167445 |
| Reference:
|
[2] P. M. Higgins: Digraphs and the semigroup of all functions on a finite set.Glasgow Math. J. 30 (1988), 41–57. Zbl 0634.20034, MR 0925558, 10.1017/S0017089500007011 |
| Reference:
|
[3] J. Konieczny: Green’s relations and regularity in centralizers of permutations.Glasgow Math. J. 41 (1999), 45–57. Zbl 0924.20049, MR 1689659, 10.1017/S0017089599970301 |
| Reference:
|
[4] J. Konieczny and S. Lipscomb: Centralizers in the semigroup of partial transformations.Math. Japon. 48 (1998), 367–376. MR 1664246 |
| Reference:
|
[5] S. Lipscomb: Symmetric Inverse Semigroups.Mathematical Surveys and Monographs, Vol. 46, American Mathematical Society, Providence, RI, 1996. Zbl 0857.20047, MR 1413301 |
| Reference:
|
[6] S. Lipscomb and J. Konieczny: Centralizers of permutations in the partial transformation semigroup.Pure Math. Appl. 6 (1995), 349–354. MR 1399299 |
| Reference:
|
[7] V. A. Liskovec and V. Z. Feĭnberg: On the permutability of mappings.Dokl. Akad. Nauk Belarusi 7 (1963), 366–369. (Russian) MR 0153609 |
| . |
