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arXiv · 2402.14529

Groups having minimal covering number 2 of diagonal type

Marco Fusari·Andrea Previtali·Pablo Spiga
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Abstract

Garonzi and Lucchini~\cite{GL} explored finite groups $G$ possessing a normal $2$-covering, where no proper quotient of $G$ exhibits such a covering. Their investigation offered a comprehensive overview of these groups, delineating that such groups fall into distinct categories: almost simple, affine, product action, or diagonal. In this paper, we focus on the family falling under the diagonal type. Specifically, we present a thorough classification of finite diagonal groups possessing a normal $2$-covering, with the attribute that no proper quotient of $G$ has such a covering.

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Marco Fusari, Andrea Previtali, Pablo Spiga. 2024-02-22. Groups having minimal covering number 2 of diagonal type. https://arxiv.org/abs/2402.14529

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