Open Access
2013 Normal coverings of linear groups
John Britnell, Attila Maróti
Algebra Number Theory 7(9): 2085-2102 (2013). DOI: 10.2140/ant.2013.7.2085


For a noncyclic finite group G, let γ(G) denote the smallest number of conjugacy classes of proper subgroups of G needed to cover G. In this paper, we show that if G is in the range SLn(q)G GLn(q) for n>2, then nπ2<γ(G)(n+1)2. This result complements recent work of Bubboloni, Praeger and Spiga on symmetric and alternating groups. We give various alternative bounds and derive explicit formulas for γ(G) in some cases.


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John Britnell. Attila Maróti. "Normal coverings of linear groups." Algebra Number Theory 7 (9) 2085 - 2102, 2013.


Received: 28 July 2012; Revised: 1 November 2012; Accepted: 14 January 2013; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1291.20024
MathSciNet: MR3152009
Digital Object Identifier: 10.2140/ant.2013.7.2085

Primary: 20D60
Secondary: 20G40

Keywords: covering , Finite group , linear group , normal covering

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 9 • 2013
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