The amplitude for double-beta decay with two-neutrino emission is related to beta- and beta+ transitions of Fermi and Gamow-Teller type connecting ground state of initial and final nuclei with virtual intermediate nuclear states. The suppression of double Fermi and Gamow-Teller matrix elements has origin in violation of the isospin SU(2) and spin-isospin SU(4) symmetries, respectively. We study double Fermi matrix elements within an exactly solvable model. By using perturbation theory up to the first order a dependence of the two-neutrino double beta decay matrix element on the like-nucleon pairing, particle-particle and particle-hole proton-neutron interactions by assuming a weak violation of isospin symmetry of Hamiltonian expressed with generators of the SO(5) group. It is found that there is a dominance of transition through a single state of the intermediate nucleus.