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A note on maximal subgroups of free idempotent generated semigroups over bands

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Abstract

We prove that all maximal subgroups of the free idempotent generated semigroup over a band B are free for all B belonging to a band variety V if and only if V consists either of left seminormal bands, or of right seminormal bands.

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References

  1. M. Brittenham, S. W. Margolis and J. Meakin, Subgroups of free idempotent generated semigroups need not be free, J. Algebra, 321 (2009), 3026–3042.

    Article  MathSciNet  MATH  Google Scholar 

  2. M. Brittenham, S. W. Margolis and J. Meakin, Subgroups of free idempotent generated semigroups: full linear monoids, manuscript, 17 pp., arXiv: 1009.5683.

  3. D. Easdown, Biordered sets of bands, Semigroup Forum, 29 (1984), 241–246.

    Article  MathSciNet  MATH  Google Scholar 

  4. D. Easdown, Biordered sets are biordered subsets of idempotents of semigroups, J. Austral. Math. Soc. Ser. A, 37 (1984), 258–268.

    Article  MathSciNet  MATH  Google Scholar 

  5. D. Easdown, Biordered sets come from semigroups, J. Algebra, 96 (1985), 581–591.

    Article  MathSciNet  MATH  Google Scholar 

  6. R. Gray and N. Ruškuc, On maximal subgroups of free idempotent generated semigroups, Israel J. Math., 189 (2012), 147–176.

    Article  MathSciNet  Google Scholar 

  7. P. M. Higgins, Techniques of Semigroup Theory, Oxford University Press, Oxford, 1992.

    MATH  Google Scholar 

  8. B. Mcelwee, Subgroups of the free semigroup on a biordered set in which principal ideals are singletons, Comm. Algebra, 30 (2002), 5513–5519.

    Article  MathSciNet  MATH  Google Scholar 

  9. K. S. S. Nambooripad, Structure of regular semigroups I, Mem. Amer. Math. Soc. Vol. 22, No. 224, Amer. Math. Soc., Rhode Island, 1979.

    Google Scholar 

  10. K. S. S. Nambooripad and F. Pastijn, Subgroups of free idempotent generated regular semigroups, Semigroup Forum, 21 (1980), 1–7.

    Article  MathSciNet  MATH  Google Scholar 

  11. N. Ruškuc, Presentations for subgroups of monoids, J. Algebra, 220 (1999), 365–380.

    Article  MathSciNet  MATH  Google Scholar 

  12. F. Pastijn, Idempotent generated completely 0-simple semigroups, Semigroup Fo-rum, 15 (1977), 41–50.

    Article  MathSciNet  MATH  Google Scholar 

  13. F. Pastijn, The biorder on the partial groupoid of idempotents of a semigroup, J. Algebra, 65 (1980), 147–187.

    Article  MathSciNet  MATH  Google Scholar 

  14. M. Petrich, The translational hull in semigroups and rings, Semigroup Forum, 1 (1970), 283–360.

    Article  MathSciNet  MATH  Google Scholar 

  15. M. Petrich, Lectures in Semigroups, Wiley, New York, 1977.

    Google Scholar 

  16. M. Petrich and P. V. Silva, Structure of relatively free bands, Comm. Algebra, 30 (2002), 4165–4187.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21101, Novi Sad, Serbia

    Igor Dolinka

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  1. Igor Dolinka
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Correspondence to Igor Dolinka.

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Communicated by Mária B. Szendrei

The support of the Ministry of Education and Science of the Republic of Serbia, through Grant No. 174019, is gratefully acknowledged.

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Dolinka, I. A note on maximal subgroups of free idempotent generated semigroups over bands. Period Math Hung 65, 97–105 (2012). https://doi.org/10.1007/s10998-012-2776-0

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  • DOI: https://doi.org/10.1007/s10998-012-2776-0

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