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 Gn can be expressed as the union of a family of proper subgroups of the same order. We prove that the answer is negative.
ANSWERING A QUESTION ON EQUALLY COVERED GROUPS
Lucchini A.
2025
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 Gn can be expressed as the union of a family of proper subgroups of the same order. We prove that the answer is negative.
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