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Semigroup Forum

, Volume 96, Issue 3, pp 565–580 | Cite as

A unifying approach to the Margolis–Meakin and Birget–Rhodes group expansion

  • Bernd Billhardt
  • Yanisa Chaiya
  • Ekkachai Laysirikul
  • Nuttawoot Nupo
  • Jintana Sanwong
Research Article
  • 86 Downloads

Abstract

Let G be a group. We show that the Birget–Rhodes prefix expansion \(G^{Pr}\) and the Margolis–Meakin expansion M(Xf) of G with respect to \(f:X\rightarrow G\) can be regarded as inverse subsemigroups of a common E-unitary inverse semigroup P. We construct P as an inverse subsemigroup of an E-unitary inverse monoid \(U/\zeta \) which is a homomorphic image of the free product U of the free semigroup \(X^+\) on X and G. The semigroup P satisfies a universal property with respect to homomorphisms into the permissible hull C(S) of a suitable E-unitary inverse semigroup S, with \(S/\sigma _S=G\), from which the characterizing universal properties of \(G^{Pr}\) and M(Xf) can be recaptured easily.

Keywords

Birget–Rhodes expansion Margolis–Meakin expansion E-unitary inverse monoid Dual prehomomorphism 

Notes

Acknowledgements

The authors are grateful to the unknown referee for helpful comments and suggestions improving the presentation of the paper.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Bernd Billhardt
    • 1
  • Yanisa Chaiya
    • 2
  • Ekkachai Laysirikul
    • 3
  • Nuttawoot Nupo
    • 2
  • Jintana Sanwong
    • 2
  1. 1.Fachbereich 10-Mathematik und Naturwissenschaften, Institut für MathematikUniversität KasselKasselGermany
  2. 2.Department of Mathematics, Faculty of ScienceChiang Mai UniversityChiang MaiThailand
  3. 3.Department of Mathematics, Faculty of ScienceNaresuan UniversityPhitsanulokThailand

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