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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Maximal subgroups of free idempotent generated semigroups over the full linear monoid


Authors: Igor Dolinka and Robert D. Gray
Journal: Trans. Amer. Math. Soc. 366 (2014), 419-455
MSC (2010): Primary 20M05; Secondary 20F05, 15A99, 57M15
Published electronically: July 24, 2013
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Abstract: We show that the rank $ r$ component of the free idempotent generated semigroup of the biordered set of the full linear semigroup full of $ n \times n$ matrices over a division ring $ Q$ has maximal subgroup isomorphic to the general linear group $ GL_r(Q)$, where $ n$ and $ r$ are positive integers with $ r < n/3$.


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Additional Information

Igor Dolinka
Affiliation: Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21101 Novi Sad, Serbia
Email: dockie@dmi.uns.ac.rs

Robert D. Gray
Affiliation: Centro de Álgebra da Universidade de Lisboa, Av. Prof. Gama Pinto, 2, 1649-003 Lisboa, Portugal
Address at time of publication: School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, United Kingdom
Email: rdgray@fc.ul.pt, Robert.D.Gray@uea.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-2013-05864-3
PII: S 0002-9947(2013)05864-3
Received by editor(s): December 6, 2011
Received by editor(s) in revised form: April 19, 2012, and April 25, 2012
Published electronically: July 24, 2013
Additional Notes: The research of the first author was supported by the Ministry of Education and Science of the Republic of Serbia through Grant No.174019, and by a grant (Contract 114–451–2002/2011) of the Secretariat of Science and Technological Development of the Autonomous Province of Vojvodina.
This work was developed within the project POCTI-ISFL-1-143 of CAUL, supported by FCT
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.