die Hinrichtung
execution
The deliberate killing of a person as the carrying out of a death sentence.
Die öffentliche Hinrichtung sollte der Abschreckung dienen.
The public execution was meant to serve as a deterrent.

execution
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execution
The deliberate killing of a person as the carrying out of a death sentence.
Die öffentliche Hinrichtung sollte der Abschreckung dienen.
The public execution was meant to serve as a deterrent.

'Die Hinrichtung' (execution) is the noun corresponding to the verb 'hinrichten' (to execute). The ending '-ung' is often used to form a feminine noun from a verb that describes the action or the result.
Die Abschaffung der Hinrichtung ist ein Zeichen für eine humane Gesellschaft.
The abolition of execution is a sign of a humane society.
Common verbs used with 'Hinrichtung' (execution) are 'vollstrecken' (to carry out), 'anordnen' (to order), or 'beiwohnen' (to attend). People also speak of 'die Vollstreckung der Hinrichtung' (the carrying out of the execution).
Der Befehl zur Hinrichtung kam direkt vom Diktator.
The order for the execution came directly from the dictator.
To name the person, the preposition 'von' (+ dative) is used. To describe the method, you use 'durch' (+ accusative).
Die Hinrichtung von politischen Gegnern war an der Tagesordnung.
The execution of political opponents was the order of the day.
death penalty
'die Todesstrafe' and 'die Hinrichtung' both belong to the topic of serious crime and state punishment. But they do not mean exactly the same thing. 'die Todesstrafe' is the punishment in the law or in the judgment: a person is to be killed as punishment. 'die Hinrichtung' is the actual carrying out of this punishment. So you can talk about the death penalty without an execution taking place. The words are easy to confuse because both are connected with death as a punishment. In practice: 'Todesstrafe' names the punishment, while 'Hinrichtung' names the act.

Die geplante Hinrichtung wurde nach neuen Beweisen gestoppt.
The planned execution was stopped after new evidence emerged.
Im Geschichtsunterricht diskutiert die Klasse über die Todesstrafe.
In history class, the class discusses the death penalty.