The word "trench warfare" does not belong with the other words because it specifically refers to a method of combat used predominantly during World War I, while the other terms—appeasement, militarism, and alliance—are related to political strategies, ideologies, or agreements that contributed to the causes of the war rather than describing a particular style of fighting.

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The term "trench warfare" is different from the others because it refers to a specific fighting method used mainly in World War I. In contrast, "appeasement," "militarism," and "alliance" are political strategies and agreements that contributed to the war's causes, not a style of combat.