Recommended reading: "In the Name of Eugenics : Genetics and the Uses of Human Heredity," by Daniel J. Kevles -- read in conjunction with The Nazi Connection: Eugenics, American Racism, and German National Socialism, by Stefan Kuhl for additional information Kevles glosses over.
It's a common mistake for people to say that the U.S. got our population control/eugenics/racism/sterilization etc., from Germany -- Germany got them from us.
And, yes, the Nazis were the Nationalsozialistische deutsche Arbeiter-Partei, the National Socialist German Workers' Party. Left-wingers.