Generating sets of finite singular transformation semigroups
Semigroup Forum, ISSN: 0037-1912, Vol: 86, Issue: 1, Page: 59-66
2013
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Article Description
J. M. Howie proved that Sing, the semigroup of all singular mappings of {1,...,n} into itself, is generated by its idempotents of defect 1 (in J. London Math. Soc. 41, 707-716, 1966). He also proved that if n≥3 then a minimal generating set for Sing contains n(n-1)/2 transformations of defect 1 (in Gomes and Howie, Math. Proc. Camb. Philos. Soc. 101. 395-403, 1987). In this paper we find necessary and sufficient conditions for any set for transformations of defect 1 in Sing to be a (minimal) generating set for Sing. © 2012 Springer Science+Business Media, LLC.
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Springer Science and Business Media LLC
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