DENVER, NOV. 10 -- The judge and jury in a federal trial involving the gangland-style murder of a Jewish talk-show host took time today to hear testimony from a rabbi about a socio-religious question that has been debated for millennia: What makes a Jew a Jew?

Rabbi Stanley Wagner of Denver's B.M.H. Synagogue was called to the witness stand as part of the government's effort to convict four white supremacists in the machine-gun slaying of Alan Berg, a radio personality who regularly attacked and taunted anti-Semitic organizations on his nightly talk show here.

Berg was gunned down in the street late one night in 1984. The MAC10 automatic pistol that killed him was later found at the secluded Idaho hideout of a small band of self-styled American Nazis. Four members of that group are on trial here -- but not on murder charges.

Bruce Carrol Pierce, David Lane, Richard Scutari and Jean Craig are accused, under the Voting Rights Act of 1968, of depriving Berg of his civil rights. U.S. District Court Judge Richard Matsch has ruled that the prosecution must prove that Berg, raised a Jew, was a Jew although he practiced no religion as an adult.

The 1968 statute prohibits discrimination based on the victim's race, religion, sex or nationality. Defense lawyers acknowledge only that Judaism is a religion -- but they argue that the "religion" clause does not cover Berg because he was not a practicing Jew.

Wagner testified today that Judaism could be considered a nationality -- "a linkage of a people, by virtue of a common history, a common culture and a common destiny . . . . A person could be born anywhere in the world" and be a Jew "by virtue of association with the people of Israel."

On the question of race, the rabbi said, "We try to eschew a racial definition. It's been foisted on us."

In a case involving vandalism against a synagogue in Silver Spring, Md., the U.S. Supreme Court last May brought Judaism within the ambit of an 1866 federal civil rights law under the "racial" category. The court ruled then that Jews constitute the type of group Congress had in mind when it barred racial discrimination.

The defendants here concede that they were outspoken anti-Semites who listened to Berg's broadcasts. But they all deny involvement in the murder. There are no eyewitnesses, and the government's case is based mainly on circumstance and on the testimony of neo-Nazis cooperating with the prosecution.

For these reasons, Denver District Attorney Norman Early concluded last year that there was not sufficient evidence to bring a murder charge. After Early's controversial decision, federal authorities obtained indictments on charges that the defendants violated Berg's civil rights by killing him.

The trial here is part of a three-act legal drama -- known informally as Operation Clean Sweep -- through which the Justice Department is hoping to crush a scattered collection of white-supremacist groups that had launched a violent drive to rid the United States of blacks, Jews and other minorities.

The first stage was a mass trial in 1985 in Seattle, where federal prosecutors obtained guilty pleas or convictions under federal racketeering statutes against 23 people connected with The Order, a heavily armed band of neo-Nazis based in northern Idaho. This month's Denver trial is the next step, and the final act is expected early next year in Fort Smith, Ark., when 14 alleged leaders of the group will go on trial on federal sedition charges.

The target of the prosecutions is a national network of hate groups. They include self-styled religious organizations such as the Idaho-based Church of Jesus Christ, Christian, and politically oriented tax-protest groups such as the Posse Comitatus, which has adherents here and there across the farm belt. Police raids on various outposts of these groups have uncovered arsenals stocked with weapons by the gross and cyanide by the gallon.

These connected anti-black, anti-Jewish groups are reportedly small in membership but grandiose in ambition. Federal agents and informants estimate that the total number of active members in all the groups probably never reached more than a few hundred. But in their meetings and on their computer bulletin boards, the activists made plans to dilute the currency through massive counterfeiting and wage violent warfare against Jewish and black leaders.

According to prosecution testimony at this trial, the murder of Alan Berg, whose talk show could be heard throughout the Rocky Mountain West, was one of the first steps in this planned war on Jews. The government charges that defendant Pierce shot Berg and escaped with help from Lane and Scutari. Craig is charged with scouting Berg's home and radio station.

Prosecutors, who rested their case today, have presented witnesses and evidence suggesting that the defendants plotted Berg's murder and boasted about the deed to friends later. Some trial participants say the defense presentation will be brief, meaning that the case could go to the jury next week.

But the defendants have said in news interviews that they hope to use this trial as a forum to explain the basis of their supremacist views -- a development that could extend the proceedings.