Maximal subgroups of free idempotent generated semigroups over the full linear monoid
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- by Igor Dolinka and Robert D. Gray PDF
- Trans. Amer. Math. Soc. 366 (2014), 419-455 Request permission
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 $r < n/3$.References
Additional Information
- Igor Dolinka
- Affiliation: Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21101 Novi Sad, Serbia
- MR Author ID: 621746
- ORCID: 0000-0002-8644-0626
- 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
- MR Author ID: 774787
- Email: rdgray@fc.ul.pt, Robert.D.Gray@uea.ac.uk
- 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 - © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 419-455
- MSC (2010): Primary 20M05; Secondary 20F05, 15A99, 57M15
- DOI: https://doi.org/10.1090/S0002-9947-2013-05864-3
- MathSciNet review: 3118401