A cover of a finite noncyclic group G is a family ℋ of proper subgroups of G whose union equals G. A cover of G is called minimal if it has minimal size, and irredundant if it does not properly contain any other cover. We classify the finite noncyclic groups all of whose irredundant covers are minimal.
Irredundant and Minimal Covers of Finite Groups
LUCCHINI, ANDREA;GARONZI, MARTINO
2016
Abstract
A cover of a finite noncyclic group G is a family ℋ of proper subgroups of G whose union equals G. A cover of G is called minimal if it has minimal size, and irredundant if it does not properly contain any other cover. We classify the finite noncyclic groups all of whose irredundant covers are minimal.
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