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arXiv · 2001.02035

On the Primary Coverings of Finite Solvable and Symmetric Groups

Francesco Fumagalli·Martino Garonzi
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Abstract

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 $\sigma_0(G)$ 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 $\sigma(G)$, the covering number, for the classes of groups $G$ that are solvable and symmetric.

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Francesco Fumagalli, Martino Garonzi. 2020-01-07. On the Primary Coverings of Finite Solvable and Symmetric Groups. https://arxiv.org/abs/2001.02035

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