No, that's a myth put forth by leftist history professors. I'm right wing and I have nothing in common with Hitler or Mussolini. They were both collectivists, whereas I support individualism. They both had complete control over their respective economies, whereas I support a free market. They both created expansive welfare states, whereas I, like all right-wingers, are against the very idea of government welfare.
Presumably you agree that Milton Friedman, Thomas Sowell, and Barry Goldwater are right wing? What do they have in common with Mussolini and Hitler? Nothing. But Hitler and Mussolini had a lot in common with modern progressives.
Yes, Hitler murdered Marxists,
but then again, so did Stalin. Leftists are naturally violent, it's not unusual for them to kill each other over trivial differences.