| Title:
|
Regular, inverse, and completely regular centralizers of permutations (English) |
| Author:
|
Konieczny, Janusz |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
179-186 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For an arbitrary permutation $\sigma $ in the semigroup $T_n$ of full transformations on a set with $n$ elements, the regular elements of the centralizer $C(\sigma )$ of $\sigma $ in $T_n$ are characterized and criteria are given for $C(\sigma )$ to be a regular semigroup, an inverse semigroup, and a completely regular semigroup. (English) |
| Keyword:
|
semigroup of full transformations |
| Keyword:
|
permutation |
| Keyword:
|
centralizer |
| Keyword:
|
regular |
| Keyword:
|
inverse |
| Keyword:
|
completely regular semigroups |
| MSC:
|
20M17 |
| MSC:
|
20M18 |
| MSC:
|
20M20 |
| idZBL:
|
Zbl 1027.20046 |
| idMR:
|
MR1995571 |
| DOI:
|
10.21136/MB.2003.134038 |
| . |
| Date available:
|
2009-09-24T22:08:24Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134038 |
| . |
| Reference:
|
[1] Higgins, P. M.: 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:
|
[2] Howie, J. M.: Fundamentals of Semigroup Theory.Oxford University Press, New York, 1995. Zbl 0835.20077, MR 1455373 |
| Reference:
|
[3] Konieczny, J.: 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] Konieczny, J.: Semigroups of transformations commuting with idempotents.Algebra Colloq. 9 (2002), 121–134. Zbl 1005.20046, MR 1901268 |
| Reference:
|
[5] Konieczny, J., Lipscomb, S.: Centralizers in the semigroup of partial transformations.Math. Japon. 48 (1998), 367–376. MR 1664246 |
| Reference:
|
[6] Liskovec, V. A., Feĭnberg, V. Z.: On the permutability of mappings.Dokl. Akad. Nauk BSSR 7 (1963), 366–369. (Russian) MR 0153609 |
| Reference:
|
[7] Liskovec, V. A., Feĭnberg, V. Z.: The order of the centralizer of a transformation.Dokl. Akad. Nauk BSSR 12 (1968), 596–598. (Russian) MR 0237624 |
| Reference:
|
[8] Weaver, M. W.: On the commutativity of a correspondence and a permutation.Pacific J. Math. 10 (1960), 705–711. Zbl 0094.03203, MR 0115923, 10.2140/pjm.1960.10.705 |
| . |
