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- Symmetries of the 2HDM: an invariant formulation and consequencesPublication . Ferreira, Pedro Miguel; Grzadkowski, B.; Ogreid, Odd Magne; Osland, P.Symmetries of the Two-Higgs-Doublet Model (2HDM) potential that can be extended to the whole Lagrangian, i.e. the CP-symmetries CP1, CP2, CP3 and the Higgs-family symmetries Z(2), U(1) and SO(3) are discussed. Sufficient and necessary conditions in terms of constraints on masses and physical couplings for the potential to respect each of these symmetries are found. Each symmetry can be realized through several alternative cases, each case being a set of relations among physical parameters. We will show that some of those relations are invariant under the renormalization group, but others are not. The cases corresponding to each symmetry group are illustrated by analyzing the interplay between the potential and the vacuum expectation values.