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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:
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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
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