Fans of Stanley Kubrick’s movie “Dr. Strangelove” will remember vividly the deranged Nazi scientist, played by Peter Sellers, struggling in vain to restrain his right arm at moments of excitement, as it involuntarily shoots upward in the Hitler salute. As the arm straightens out and reaches an angle of 45 degrees, it reminds us in a single image not just that some military scientists in postwar America had started their careers in Nazi Germany, but also that giving the Hitler salute had become second nature to the people who supported Hitler and his regime. That gesture is the topic of “The Hitler Salute” (Metropolitan Books, 128 pages, $20), by the German sociologist Tilman Allert, expertly translated into thoroughly readable English by Jefferson Chase. Mr. Allert reminds us that rendering the gesture — accompanied by the words “Heil Hitler!” and, if you were a storm trooper wearing a serviceable pair of jackboots, a sharp clicking together of the heels — quickly became compulsory under the Nazis. By the summer of 1933, the Nazis’ first year in power, all civil servants were required to use it in person, when encountering each other, or on paper, where the words “Heil Hitler!” replaced the conventional “sincerely” and similar signing-off formulae.

On the street, Germans were supposed to use the Hitler greeting instead of “Good morning!” Postmen were meant to bark out a “Heil Hitler!” to customers before handing them their morning mail. Schoolchildren greeted their teachers every morning with “Heil Hitler!” One of the many entertaining illustrations in the book shows a wall painting from a German school depicting the prince greeting Sleeping Beauty not with a kiss, but with a Hitler salute. The gesture had become ubiquitous and inescapable.

But what exactly did it mean? “Heil!” didn’t just mean “Hail!”; the word also carried connotations of healing, health, and good wishes. “Heil Hitler!” therefore involved implicitly wishing the Nazi Leader good health, and also invoking Hitler as a kind of Supreme Being who could grant good health to the greeting’s recipient. In both cases, Hitler was introduced as an omnipresent third party whenever two Germans came across each other. People were aware of these added meanings, and some at least made fun of them. Treating “Heil!” as a command rather than a wish (“Heal Hitler!”), you could reply to the greeting by saying, “Heal him yourself,” implying that the Nazi leader was sick, or mentally ill; or you could feign innocence when somebody said “Heil Hitler!” to you by asking: “What’s he got to do with it?”, thus implying that the salutation was unnecessary and out of place.

Moving your right arm up swiftly and stiffly to the required angle meant you had to step back from the object of your salute to avoid an accident (it was said that when the Nazi ambassador to London, Joachim von Ribbentrop, was presented at court, he thoroughly alarmed the shy, stuttering King George VI by barking out “Heil Hitler!” to him and narrowly missing the monarch’s nose as he swept his right arm upward in a smart Nazi salute; no wonder the ambassador quickly became known as “Von Brickendrop”). The distance this created replaced the intimacy of shaking hands and alienated people from one another, uniting them only in their allegiance to Hitler.

The Hitler salute was also routinely described as the “German greeting”; giving it was a signal of national identity. From 1937, indeed, Jews were banned from using it, so that the greeting became an emblem of supposed racial superiority and togetherness. In Catholic southern Germany, where people conventionally said hello to one another with the words “Gruss Gott!” — “God’s greeting!” — it gave the Nazi leader divine status by replacing “God” with “Hitler.” The salute thus replaced regional differences in greeting formulae — which varied from “Servus” in the south to “Moin-Moin” on the northern coastline — with a nationwide gesture, affirming people’s collective identity above all as Germans, a single race united in a single Nazi cause.

The salute brought the regime into every aspect of daily life. With everybody using it, those who were perhaps initially reluctant could feel hopelessly outnumbered. Eventually they, too, felt there was no alternative to it, and the implications of this were far-reaching. When rendered in public, the “German greeting” militarized human encounters; it stamped individuals as members of a society mobilizing under Nazi leadership for war, and indeed it reduced people’s sense of their own individuality, and thus undermined their ability to take moral responsibility for their actions, placing the responsibility in the hands of Hitler instead.

Mr. Allert brings out these multiple meanings of the Hitler salute with a good deal of persuasiveness. Running through this book, however, is a palpable tension between the sociologist’s love of the sweeping generalization and the historian’s respect for particular, often obstinately recalcitrant facts. Mr. Allert the sociologist wants us to believe that the Hitler greeting became a universal signifier of Germans’ abandonment of established communities and institutions, such as the church, the army, and the family, and that Nazi Germany became a nation of conformists, who abandoned their primary social allegiances with a simple and singular allegiance to Hitler. But Mr. Allert the historian knows that in fact it was all a lot more complicated than that.

To begin with, people often rendered the gesture under duress. Particularly in the first months of Nazi power, when dissidents and opponents of the regime were liable to be beaten up by storm troopers or hauled off to a concentration camp, many people conformed simply out of fear. The posters put up along Germany’s streets proclaiming “Germans use the German Greeting!” implied that anyone who did not use it could not be counted as part of the “national community” of Germans, and was an outsider, an outcast, even an enemy. The journalist Charlotte Beradt was told by a former socialist acquaintance at this time that he had dreamed that Nazi Propaganda Minister Joseph Goebbels had visited him at his workplace, but that he had found it extremely difficult to raise his right arm to the minister in the Nazi salute; he managed it eventually after half an hour of trying, only to be told by Goebbels, coldly: “I don’t want your salute.” Here in a single anecdote was all the fear, anxiety, and doubt that characterized many non-Nazi Germans’ attitudes toward the salute at the outset of the Third Reich. Even at this time, however, and increasingly as time went on, people often used a conventional greeting as before, following up the Hitler salute with a “Good Day” and a handshake. Mr. Allert mentions this practice, but he does not discuss it further; yet it undermines his whole argument because it implies that people regarded “Heil Hitler!” as a more or less irritating formality, to be gotten out of the way before you said your real hello, reconnecting yourself to your friend, relative, colleague, or acquaintance and restoring the customary bonds of sociability that had briefly been violated by the formal gesture of the Nazi salute. In any case, people very soon stopped using the Hitler salute, once the initial period of violence and intimidation was over. Visitors to Berlin were already noting in the mid-1930s that the salute had become less common than before. One narrow street in Munich is still known even today as “Shirkers’ Alley” because people dodged through it in order to avoid having to salute a nearby Nazi monument. In October 1940, when it was clear that Germany was not going to bomb the British into submission, CBS correspondent William L. Shirer observed that people in Munich had “completely stopped saying Heil Hitler!” After the German defeat in the Battle of Stalingrad, the SS security service reported that people were no longer using the “German greeting,” and indeed it had virtually disappeared, except among Nazi Party fanatics, by the end of the war. Even when they had to use it, Germans could sometimes turn it into a gesture of defiance against the regime. In 1934, traveling circus performers were put under police surveillance after reports that they had been training their monkeys to give the salute. And a photograph exists of miners in the Bavarian town of Penzberg, assembled for a ceremonial parade, waving their arms about in all kinds of ways, ignoring the Hitler Youth contingent standing behind them, showing how it really should be done.

In the end, Mr. Allert the historian knows well enough, as he concedes toward the end of this fascinating little book, that “it would be too simple to read the gesture as a sign of unambiguous support.” The fact that people “saluted opportunistically, defensively, or even to express resistance, albeit veiled and modest,” combined with the fact that Germans increasingly often refused or neglected to salute, or nullified the salute’s effect by following it with a conventional greeting, gives the lie to his claim that the salute itself brought about a “breakdown in people’s sense of self,” helped Germans “evade the responsibility of normal social intercourse, rejected the gift of contact with others, allowed social mores to decay, and refused to acknowledge the inherent openness and ambivalence of human relationships and social exchange.” Life isn’t as simple as that, even if sociologists sometimes think it is.

Mr. Evans is a professor of modern history at the University of Cambridge and the author of “The Third Reich in Power.” His book “The Third Reich at War” is forthcoming from Penguin Press.