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On properties of group closures of one-to-one transformations

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

Inessa Levi
Inessa Levi
Affiliation:
Department of Mathematics, Morgan Hall 118, 1 University Circle, Western Illinois University, Macomb, IL 61455-1390, USA, e-mail: [email protected]
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Abstract

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For a permutation group H on an infinite set X and a transformation f of X, let 〈f: H〉 = 〈{hfh-1:h є; H}〉 be a group closure of f. We find necessary and sufficient conditions for distinct normal subgroups of the symmetric group on X and a one-to-one transformation f of X to generate distinct group closures of f. Amongst these group closures we characterize those that are left simple, left cancellative, idempotent-free semigroups, whose congruence lattice forms a chain and whose congruences are preserved under automorphisms.

Keywords

semigrouptransformationpermutation groupconjugatescentralizercongruencecongruence latticeleft simpleautomorphism groupinner automorphism.

MSC classification

Secondary: 20M20: Semigroups of transformations, etc.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 79 , Issue 2 , October 2005 , pp. 213 - 229
Copyright
Copyright © Australian Mathematical Society 2005

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