Finite groups are big as semigroups

Igor Dolinka, Nik Ruskuc

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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.
Original languageEnglish
Pages (from-to)209-217
Number of pages9
JournalArchiv der Mathematik
Issue number3
Early online date30 Aug 2011
Publication statusPublished - Sept 2011


  • Finite maximal subsemigroup
  • Rees matrix semigroup


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