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A neat story but let us not forget our own Christie Pitts riots wherein the local Jews, along with their Italian allies, took on the local Swastika Club in a six hour battle up and down the streets of Toronto.
Another exemplary gangland fighter against the Hun was Monk Eastman - last of the Old Tyme Gangsters. He was drafted into the American forces in World War One and demonstrated time and time again the skills that had made him one of the most feared gangsters in New York. Once the Sargent pointed him towards some German "bunch of guys trying to muscle in on our territory" they were doomed. Machine gun nest, mortar battery or just plain old rifle platoon it didn't matter - Monk just bumped them off as if it was just another day at the office in his old gangland haunts. He was also the model for every caricatured gangster wearing a much-too-small derby on his head: like that bulldog in Bugs Bunny.
His, and Lansky's, superior in the Underworld was the definitive Jewish Crimelord Arnold "The Brain" Rothstein. Like all those guys who say "But Daaad, I don't want to be a Cantor; I want to be a singer/standup comedian/clown/gangster" he, of course, ended up being an archetypal example of his chosen profession and redefined said profession in the process. He's credited with the invention of the modern Crime Syndicate.
Sadly for those of use who grew up on Wonder Woman and so on, there was no vast network of Nazi Spies in league with Bundists anywhere in Allied territory. A post-war check of Nazi records shows that they never managed to insert a single operative that we didn't turn into a double agent. The only sort-of-counter-example was Henri Dericourt who might have been a double agent inside the British SOE for the German SD but possible also a triple agent for MI6 on top of all of that.