Largest subsemigroups of the full transformation monoid

R. Gray; J. D. Mitchell

doi:10.1016/j.disc.2007.08.075

Largest subsemigroups of the full transformation monoid

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Abstract

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 language	English
Pages (from-to)	4801-4810
Number of pages	10
Journal	Discrete Mathematics
Volume	308
Issue number	20
DOIs	https://doi.org/10.1016/j.disc.2007.08.075
Publication status	Published - 28 Oct 2008

Keywords

transformation semigroups
completely simple semigroups
inverse semigroups
SEMIGROUPS
SUBGROUPS

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10.1016/j.disc.2007.08.075

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KW - completely simple semigroups

KW - inverse semigroups

KW - SEMIGROUPS

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Largest subsemigroups of the full transformation monoid

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Keywords

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