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Finite groups are big as semigroups

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Abstract

We prove that a finite group G occurs as a maximal proper subsemigroup of an infinite semigroup (in the terminology of Freese, Ježek, and Nation, G is a big semigroup) if and only if |G| ≥ 3. In fact, any finite semigroup whose minimal ideal contains a subgroup with at least three elements is big.

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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

    I. Dolinka

  2. School of Mathematics and Statistics, University of St Andrews, St Andrews, KY16 9SS, Scotland, UK

    N. Ruškuc

Authors
  1. I. Dolinka
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  2. N. Ruškuc
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Correspondence to I. Dolinka.

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Dedicated to the memory of Jaroslav Ježek (1945–2011)

The research of the first author is supported by the Ministry of Education and Science of the Republic of Serbia through Grant No.174019, and by a grant (Contract 114-451-2002/2011) of the the Secretariat of Science and Technological Development of the Autonomous Province of Vojvodina.

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Dolinka, I., Ruškuc, N. Finite groups are big as semigroups. Arch. Math. 97, 209–217 (2011). https://doi.org/10.1007/s00013-011-0297-3

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  • DOI: https://doi.org/10.1007/s00013-011-0297-3

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