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The affine and projective groups are maximal


Authors: Itay Kaplan and Pierre Simon
Journal: Trans. Amer. Math. Soc. 368 (2016), 5229-5245
MSC (2010): Primary 03C40, 51E15, 51E10, 20E28, 20B27
Published electronically: November 12, 2015
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Abstract: We show that the groups $ AGL_{n}\left (\mathbb{Q}\right )$ (for $ n\geq 2$) and $ PGL_{n}\left (\mathbb{Q}\right )$ (for $ n\geq 3$), seen as closed subgroups of $ S_{\omega }$, are maximal-closed.


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Additional Information

Itay Kaplan
Affiliation: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel
Email: kaplan@math.huji.ac.il

Pierre Simon
Affiliation: Institut Camille Jordan, Université Claude Bernard - Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne Cedex, France
Email: simon@math.univ-lyon1.fr

DOI: https://doi.org/10.1090/tran/6608
Received by editor(s): December 1, 2013
Received by editor(s) in revised form: October 15, 2014
Published electronically: November 12, 2015
Additional Notes: The first author would like to thank the Israel Science foundation for partial support of this research (Grant no. 1533/14).
The research leading to these results received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007- 2013)/ERC Grant Agreement No. 291111.
Article copyright: © Copyright 2015 American Mathematical Society