• In May, a Florida teenager, Devon Arthurs, told the police he had killed two of his neo-Nazi roommates for disrespecting his Muslim faith. (He had recently converted.) His arrest led to the discovery that a fourth roommate, Brandon Russell, had been stockpiling explosive material. Mr. Russell, who told law enforcement officials he was a member of Atomwaffen, was revealed to be a founding member of the group, and was sentenced to five years in prison for having stockpiled the explosives.

• In December, a husband and wife were shot dead in their Virginia home three days before Christmas by a teenage neo-Nazi. The suspect was identified by HuffPost as Nicholas Giampa, which found him to have been influenced by neo-Nazi literature republished online by Atomwaffen.

• Last month, ProPublica reported that Samuel Woodward, who has been charged with the murder of a college student, Blaze Bernstein, was a member of the group.

The organization has promoted its cause on college campuses in Washington, Pennsylvania and Illinois, according to the Anti-Defamation League.

Is the F.B.I. investigating Atomwaffen?

An F.B.I. spokesman would not comment directly.

“The F.B.I. does not and will not police ideology, but has been investigating the criminal activities of white supremacy extremists for nearly a century,” he said. “When an individual takes violent action based on belief or ideology and breaks the law, the F.B.I. will enforce the rule of law.”

In an interview Friday, Danny Coulson, the former deputy assistant director of the F.B.I., explained that the bureau was somewhat constrained in what it could do when no violence had been committed.

Mr. Coulson was one of the leaders of the investigation into the 1995 bombing of the federal building in Oklahoma City by Timothy McVeigh, who is much admired in Atomwaffen literature. He also led the operation that ended in the death of the neo-Nazi leader Robert Jay Mathews and helped bring to justice the white supremacists of the Covenant, Sword and Arm of the Lord.