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Every coprime linear group admits a base of size two


Authors: Zoltán Halasi and Károly Podoski
Journal: Trans. Amer. Math. Soc. 368 (2016), 5857-5887
MSC (2010): Primary 20C15; Secondary 20B99
Published electronically: December 15, 2015
MathSciNet review: 3458401
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Abstract: Let $ G$ be a linear group acting faithfully on a finite vector space $ V$ and assume that $ (\vert G\vert,\vert V\vert) =1$. In this paper we prove that $ G$ admits a base of size two and that this estimate is sharp. This generalizes and strengthens several former results concerning base sizes of coprime linear groups. As a direct consequence, we answer a question of I. M. Isaacs in the affirmative.


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Additional Information

Zoltán Halasi
Affiliation: Institute of Mathematics, University of Debrecen, P.O. Box 12, H-4010 Debrecen, Hungary
Address at time of publication: Department of Algebra and Number Theory, Eötvös University, Pázmány Péter sétány 1/c, 1117 Budapest, Hungary
Email: halasi.zoltan@renyi.mta.hu

Károly Podoski
Affiliation: Budapest Business School, College of Finance and Accountancy, Buzogány Street 10-12, H-1149 Budapest, Hungary
Address at time of publication: Alfréd Rényi Institute of Mathematics, Hungarian Academy of Sciences, Reáltanoda u. 13-15, 1053 Budapest, Hungary
Email: podoski.karoly@pszfb.bgf.hu, podoski.karoly@renyi.mta.hu

DOI: https://doi.org/10.1090/tran/6544
Keywords: Coprime linear group, base size, regular partition
Received by editor(s): December 26, 2013
Received by editor(s) in revised form: June 30, 2014, and August 3, 2014
Published electronically: December 15, 2015
Additional Notes: The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 318202, from MTA Rényi Institute Lendület Limits of Structures Research Group and from OTKA K84233.
Article copyright: © Copyright 2015 American Mathematical Society