Stable exponential cosmological solutions with zero variation of $G$ and three different Hubble-like parameters in the Einstein-Gauss-Bonnet model with a $\mathrm{\Lambda }$-term

We consider a $D$-dimensional gravitational model with a Gauss-Bonnet term and the cosmological term $\mathrm{\Lambda }$. We restrict the metrics to diagonal cosmological ones and find for certain $\mathrm{\Lambda }$ a class of solutions with exponential time dependence of three scale factors, governed by three non-coinciding Hubble-like parameters $H>0$, $h_1$ and $h_2$, corresponding to factor spaces of dimensions $m>2$, $k_1>1$ and $k_2>1$, respectively, with $k_1\mathrm{\ne }{k}_2$ and $D=1+m+k_1+k_2$. Any of these solutions describes an exponential expansion of $3d$ subspace with Hubble parameter $H$ and zero variation of the effective gravitational constant $G$. We prove the stability of these solutions in a class of cosmological solutions with diagonal metrics.