Low-lying structures in the Gamow-Teller strength functions for the double-beta-decaying nuclei<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Ge</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>76</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Se</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>82</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Te</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>128</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>, and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi mathvariant="normal">Te</mml:mi></mml:mrow><mml:mprescripts/><mml:mrow/><mml:mrow><mml:mn>130</mml:mn></mml:mrow><mml:mrow/><mml:mrow/></mml:mmultiscripts></mml:mrow></mml:math>

Excitation-energy distributions of transition strength to ${1}^{+}$ states excited via the (p,n) reaction at 134.4 MeV on targets of $^{76}\mathrm{Ge}$, $^{82}\mathrm{Se}$, $^{128}\mathrm{Te}$, and $^{130}\mathrm{Te}$ were measured for excitation energies up to 25 MeV. Structures observed in the neutron spectra with forward-peaked (\ensuremath{\Delta}L=0) angular distributions were identified as ${1}^{+}$ states, except for the isobaric analog transitions. The total ${1}^{+}$ strength in these reactions was extracted by normalizing the intensity in the ${1}^{+}$ peaks to the Fermi transition strength observed in the isobaric analog state. The Gamow-Teller strength observed in ${1}^{+}$ peaks above a fitted polynomial background is typically 55% of the sum rule obtained by assuming that the strength of ${\ensuremath{\beta}}^{+}$ transitions is negligible. The portion of this strength found at excitation energies less than that of the Gamow-Teller giant resonance varied from 15% for $^{128}\mathrm{Te}$ to 38% for $^{76}\mathrm{Ge}$. Experimental results are compared with predictions of a shell model that includes a pairing force and a long-range Gamow-Teller force in both parent and daughter nuclei. A comparison of the strength functions of the tellurium isotopes is made; this comparison is relevant in determining whether double-beta decay without neutrino emission (0\ensuremath{\nu} decay) is observed in these isotopes.