<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="script">T</mml:mi><mml:mo>,</mml:mo><mml:mi mathvariant="script">P</mml:mi></mml:mrow></mml:math> -odd effects in the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mi>LuOH</mml:mi></mml:mrow><mml:mo>+</mml:mo></mml:msup></mml:math> cation

The LuOH$^+$ cation is a promising system to search for manifestations of time reversal and spatial parity violation effects. Such effects in induced by the electron electric dipole moment $e$EDM scalar-pseudoscalar interaction nucleus with electrons, characterized $k_s$ constant, are studied. enhancement factors, polarization external field, hyperfine interaction, rovibrational structure calculated. study required experiment preparation extraction eEDM ks values from experimental data.