Via Starwars.com:

An Emperor is nothing without the support of ground forces to enforce their will. These troops must be unquestionably loyal to the cause and its leader. In the Star Wars galaxy, that task falls to the Imperial stormtroopers. This faceless corps of soldiers was inspired by the similar storm troops from the past.

While most well-known “storm troops” were the Nazi Sturmabteilung, the formation of “storm troop” units predates the National Socialists or World War II. In Germany, the SA (Sturmabteilung) took its name from the small units of storm troops used in German offensives of World War I. When the First World War turned into a trench-laden stalemate, both sides looked for new ways to break through enemy defenses. Organized into small units of fast moving soldiers and often armed with grenades, these original storm troops were trained to quickly break through enemy lines using stealth and surprise to their advantage.

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