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arXiv · 1903.05187

Linear bounds for the normal covering number of the symmetric and alternating groups

Daniela Bubboloni·Cheryl E. Praeger·Pablo Spiga
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Abstract

The normal covering number $γ(G)$ 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 $γ(S_n)$, when $n$ is even, and for $γ(A_n)$, when $n$ is odd.

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Daniela Bubboloni, Cheryl E. Praeger, Pablo Spiga. 2019-03-12. Linear bounds for the normal covering number of the symmetric and alternating groups. https://doi.org/10.1007/s00605-019-01287-5

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