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arXiv 2001.020352020-01math.GR

On the Primary Coverings of Finite Solvable and Symmetric Groups

Francesco Fumagalli, Martino Garonzi

英文摘要：

A primary covering of a finite group $G$ is a family of proper subgroups of $G$ whose union contains the set of elements of $G$ having order a prime power. We denote with $σ_0(G)$ the smallest size of a primary covering of $G$, and call it the primary covering number of $G$. We study this number and compare it with its analogous $σ(G)$, the covering number, for the classes of groups $G$ that are solvable and symmetric.

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