The experiment that showed that people will obey authority is the:

The Milgram experiment.

Explanation:

The Milgram experiment was carried out  to determine obedience to authority figures.

Stanley Milgran, a Yale University psychologist, instructed students to perform tasks that were in conflict with their personal conscience. They had to administer electric shocks to a person called 'learner'. In the end, the intensity of the shocks would kill the 'learner'.

The experiment found out that the majority of the participants would obey the instruction without questioning the order, even if it meant the death of the 'learner'.

This experiment was often used as an example of blind following in Nazi Germany.