There was nothing
socialist, in the sense I use the term, about
Nazi Germany.
Mussolini had a name for
Fascism and it was the "
corporate state".
Industry was privately owned, although the captains of
industry were in collusion with the government, because
war economy == big profits.
Socialism implies -- or should imply -- worker control of industry. It is only a testament to the cogency of the socialist ideal that practically every political party outside the US claims to adhere to it. Whether nationalization without, or even with, democratic controls is socialism is
debatable.
It's just as naive to consider the
USSR socialist and
soviet as to consider it a
union of
republics. Next you'll tell me
democracy is inherently
totalitarian because of the
German Democratic Republic.
What the Nationalist Socialist rank-and-file did advocate was a Bolshevik-style nationalization of industry. Hitler put the kabosh on this with the
Night of the Long Knives.