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Full-Text Articles in Applied Mathematics
Groups Expressed As The Set-Theoretic Union Of Proper Subgroups, Lana Barrett
Groups Expressed As The Set-Theoretic Union Of Proper Subgroups, Lana Barrett
Masters Theses & Specialist Projects
In their paper “Groups as Unions of Proper Subgroups,” published in 1959, Haber and Rosenfeld posed the problem of characterizing groups which can be expressed as the set theoretic union of a finite collection of their proper subgroups. Haber and Rosenfeld established that a group G is the union of three proper subgroups (such a group G shall be called a U3-group) if and only if the Klein 4-group is a homomorphic image of G. Further results concerning U3-groups were obtained in the paper “Groups which are the Union of Three Subgroups” by Bruckhemier, Bryan and …