Linear bounds for the normal covering number of the symmetric and alternating groups
Bubboloni, Daniela ; Praeger, Cheryl E. ; Spiga, Pablo
The normal covering number ▫$\gamma (G)$▫ of a finite, non-cyclic group ▫$G$▫ is the minimum number of proper subgroups such that each element of ▫$G$▫ lies in some conjugate of one of these ...subgroups. We find lower bounds linear in ▫$n$▫ for ▫$\gamma (S_n)$▫, when ▫$n$▫ is even, and for ▫$\gamma (A_n)$▫, when ▫$n$▫ is odd.
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