Largest subsemigroups of the full transformation monoid

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4 Citations (Scopus)


In this paper we are concerned with the following question: for a semigroup S, what is the largest size of a subsemigroup T <= S where T has a given property? The semigroups S that we consider are the full transformation semigroups; all mappings from a finite set to itself under composition of mappings. The subsemigroups T that we consider are of one of the following types: left zero, fight zero, completely simple. or inverse. Furthermore, we find the largest size of such subsemigroups U where the least rank of an element in U is specified. Numerous examples are given. (C) 2007 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)4801-4810
Number of pages10
JournalDiscrete Mathematics
Issue number20
Publication statusPublished - 28 Oct 2008


  • transformation semigroups
  • completely simple semigroups
  • inverse semigroups


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