Answering a question on equally covered groups

Abstract

Foguel, Moghaddamfar, Schmidt, and Velasquez-Berroteran asked in [Int. Electron. J. Algebra, 37(2025), 352-365] whether there exists a positive integer $n$ with the property that, for every finite group $G$, the Cartesian power $G^n$ can be expressed as the union of a family of proper subgroups of the same order. We prove that the answer is negative.

Keywords

• Equally covered group
• Cartesian power of a group
• PSL(2,p)

References

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