Leírás
Abstract:
In this talk I will present the content of a recent paper joint with my student Michell L. Dias. If G is a finite group, a partition of G is a family of proper subgroups of G whose union is G and such that the intersection of any two of its members is trivial. An easy example is given by Frobenius groups: the family consisting of the Frobenius kernel and the Frobenius complements is a partition. A group admitting a partition is called partitionable, and this is a very restrictive condition. Partitionable groups were classified by Baer, Kegel and Suzuki in 1961. Call s(G) the minimal size of a family of proper subgroups of G whose union is G. We classified the finite groups G which have a partition of size s(G). We also studied the minimal size of a partition of a partitionable group, calculating its precise value in some relevant cases.
DOI: 10.1016/j.jalgebra.2019.04.017
Arxiv link: https://arxiv.org/abs/1811.02996
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