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Green’s relations and regularity in centralizers of permutations

Published online by Cambridge University Press:  19 July 2001

JANUSZ KONIECZNY
JANUSZ KONIECZNY
Affiliation:
Department of Mathematics, Mary Washington College, Fredericksburg, Virginia 22401, USA; e-mail: jkoniecz@mwcgw.mwc.edu
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Abstract

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For any permutation σ on N = {1,2,…,n}: (i) Green’s relations are characterized in the centralizer C(σ) of σ (relative to the semigroup PTn of partial transformations on N); and (ii) a criterion is given for C(σ) to be a regular semigroup (inverse semigroup, union of groups).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 41 , Issue 1 , March 1999 , pp. 45 - 57
Copyright
1999 Glasgow Mathematical Journal Trust