Though this was couched as part of Mr. Trump’s tirade against “radical Islam,” the reference to honor killings implied that Muslim culture as a whole is morally flawed and dangerous. This is despite the fact that honor killings are not exclusive to Muslim societies. Many occur in India, a mostly Hindu country — something Mr. Trump ignored as he used such examples to bolster his argument for restrictions on Muslim immigration to the United States.

A similar flawed logic was used to defend lynching in the South: Black men, the theory went, by some innate nature threatened the honor and safety of white women. But historians have documented that many black men who were lynched had not even been accused of rape. Rather, the deaths were a product of the portrayal of black men as an undifferentiated mass who had to be terrorized into submission.

“The myth insisted that black men were driven to assault white women and that, as a deterrent, ‘black beast rapists’ should pay with their lives,” wrote Lisa Lindquist-Dorr, a historian, in her book, “White Women, Rape and the Power of Race in Virginia, 1900-1960.” “For whites, responding to black men’s alleged assaults was both a means of racial control and a way to assert white supremacy.”

Similarly, in 1930s Spain, nationalist propaganda falsely claimed that republican fighters had raped nuns during the civil war. Because nuns held an especially respected position in Catholic Spain, the accusations served to demonize the republican forces as monstrous, and to generate support for Franco’s nationalists.

Britain’s use in World War I of lurid tales of rapist soldiers was part of a campaign to pressure the United States into joining the war effort. Once the United States joined, American propaganda used the same imagery to encourage people to enlist. One poster portrayed Germany as a giant ape, carrying a swooning woman in one arm and a club in the other. Its tagline read, “Destroy this mad brute: enlist!”