Pz is Panzer. Panzer Division is Armoured or Tank Division. The word panzer actually translates as armoured rather than tank.
Abt is short for Abteilung. Its usually refers to a battalion sized independent unit, such as those that deployed Tiger tanks. The best translation would be detachment.
For example, the 501. s. Pz. Abt would be the 501. schwere Panzer Abteilung or 501st Heavy Tank Detachment.
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