#### Vol. 7, No. 9, 2013

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Normal coverings of linear groups

### John R. Britnell and Attila Maróti

Vol. 7 (2013), No. 9, 2085–2102
##### Abstract

For a noncyclic finite group $G$, let $\gamma \left(G\right)$ 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 ${SL}_{n}\left(q\right)\le G\le {GL}_{n}\left(q\right)$ for $n>2$, then $n∕{\pi }^{2}<\gamma \left(G\right)\le \left(n+1\right)∕2$. 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 $\gamma \left(G\right)$ in some cases.

##### Keywords
covering, normal covering, linear group, finite group
Primary: 20D60
Secondary: 20G40