For a noncyclic finite group , let denote the smallest number of conjugacy classes of proper subgroups of needed to cover . In this paper, we show that if is in the range for , then . 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 in some cases.
John Britnell. Attila Maróti. "Normal coverings of linear groups." Algebra Number Theory 7 (9) 2085 - 2102, 2013. https://doi.org/10.2140/ant.2013.7.2085