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Normal coverings of linear groups

Lookup NU author(s): Dr John Britnell

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Abstract

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.

Publication metadata

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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