Impact of the equation of state on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>f</mml:mi></mml:mrow></mml:math> - and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>p</mml:mi></mml:math> - mode oscillations of neutron stars

We investigate the impact of neutron-star matter equation state on $f$- and $p_1$-mode oscillations neutron stars obtained within Cowling approximation linearized general relativity. The oscillation frequencies, their damping times are calculated using representative sets Skyrme Hartree-Fock relativistic mean-field models, all which reproduce nuclear systematics support $2M_\odot$ stars. Our study shows strong correlations between frequencies $p_1$-modes with pressure $\beta$-equilibrated at densities equal to or slightly higher than saturation density $\rho_0$. Such found be almost independent composition frequency $1.4M_\odot$ star is strongly correlated slope symmetry energy $L_0$ Compared GR calculations, error in for $f$-mode about 30\% low mass, whereas it decreases increasing mass. accuracy better 15\% maximum improves lower masses number radial nodes.