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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 n/π2 < 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. © 2013 Mathematical Sciences Publishers.
Author(s): Britnell JR, Maroti A
Publication type: Article
Publication status: Published
Journal: Algebra and Number Theory
Year: 2013
Volume: 7
Issue: 9
Pages: 2085-2102
Online publication date: 18/12/2013
ISSN (print): 1937-0652
ISSN (electronic): 1944-7833
Publisher: Mathematical Sciences Publishers
URL: https://doi.org/10.2140/ant.2013.7.2085
DOI: 10.2140/ant.2013.7.2085
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