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Finite groups are big as semigroups

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fG_bigSG_final.pdf (295.3Kb)
Date
09/2011
Author
Dolinka, Igor
Ruskuc, Nik
Funder
EPSRC
Grant ID
EP/H011978/1
Keywords
Finite maximal subsemigroup
Rees matrix semigroup
QA Mathematics
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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.
Citation
Dolinka , I & Ruskuc , N 2011 , ' Finite groups are big as semigroups ' , Archiv der Mathematik , vol. 97 , no. 3 , pp. 209-217 . https://doi.org/10.1007/s00013-011-0297-3
Publication
Archiv der Mathematik
Status
Peer reviewed
DOI
https://doi.org/10.1007/s00013-011-0297-3
ISSN
0003-889X
Type
Journal article
Rights
This is an author version of this article. The original publication is available at www.springerlink.com copyright (c) 2011 Springer Basel AG.
Collections
  • Centre for Interdisciplinary Research in Computational Algebra (CIRCA) Research
  • Mathematics & Statistics Research
  • University of St Andrews Research
URI
http://hdl.handle.net/10023/2004

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