Groups having minimal covering number 2 of the diagonal type

Marco Fusari, Andrea Previtali and Pablo Spiga

Mathematische Nachrichten, 2024, vol. 297, issue 8, 2918-2926

Abstract: Garonzi and Lucchini explored finite groups G$G$ possessing a normal 2‐covering, where no proper quotient of G$G$ 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$G$ has such a covering. With deep appreciation to Martino Garonzi and Andrea Lucchini, for keeping us entertained.

Date: 2024
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https://doi.org/10.1002/mana.202400096

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