Complex sentence: It took part in Operation Mars alongside the 22nd Army, then in the Battle of Kursk, then fought across the Ukraine with the Central, Belorussian, and 1st Belorussian Fronts.
Split into simpler sentences: It took part in Operation Mars alongside the 22nd Army. The Corps then fought in the Battle of Kursk, then fought across the Ukraine with the Central, Belorussian, and 1st Belorussian Fronts.