A cover of a finite group G is a family of proper subgroups of G whose union is G, and a cover is called minimal if it is a cover of minimal cardinality. A partition of G is a cover such that the intersection of any two of its members is {1}. In this paper we determine all finite groups that admit a minimal cover that is also a partition. We prove that this happens if and only if G is isomorphic to C p ×C p for some prime p or to a Frobenius group with Frobenius kernel being an abelian minimal normal subgroup and Frobenius complement cyclic.
Group partitions of minimal size
Garonzi, Martino
;
2019
Abstract
A cover of a finite group G is a family of proper subgroups of G whose union is G, and a cover is called minimal if it is a cover of minimal cardinality. A partition of G is a cover such that the intersection of any two of its members is {1}. In this paper we determine all finite groups that admit a minimal cover that is also a partition. We prove that this happens if and only if G is isomorphic to C p ×C p for some prime p or to a Frobenius group with Frobenius kernel being an abelian minimal normal subgroup and Frobenius complement cyclic.File in questo prodotto:
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