Not specifically means of production, but money. Socialism is when the government controls the money. For example, I can say Canada's universal health care is socialist because the government controls how it's funded. It doesn't matter that 99.999% of clinics are privately owned. They are government funded through taxation, therefore it is socialist. Roads are socialist too, even though roads are made by private companies.
Are certain functions of the government "socialist" just because they perform it instead of the market? Adam Smith writes in the Wealth of Nations, that some functions must be performed by the government because the market is ineffective when it comes to those functions. They might be "socialist" in the sense that it is benefiting all and the cost is absorbed by the tax payer, but that's not the only part of political system of socialism.
The claim being made here is that Hitler was a socialist - that's total baloney. In socialism, the power comes from the bottom up - the working class. Through the gaining control of where they can earn their living, they can control the rest of government. Democracy is a natural ally of socialism.
Hitler may have had policies that benefited Germany, but he was an authoritarian dictator. By that definition, he couldn't be socialist, because the workers had no power. Sure, some of the industries were nationalized, but they weren't nationalized for the benefit of society and the worker, they were nationalized so that Germany could prepare for war and steamroll its neighbors. True socialists and communists were sent off to concentration camps under Hitler.
And just because it was labeled National Socialism, doesn't make it so. It started off as a more right- than most socialist party, but when Hitler took over, it talked out of both sides of the mouth. To workers, he would destroy industry and to the middle class and well-to-do, he would protect private property.
How much do the workers really own in any socialist system? The production is owned by the public but run by the govt. Which is usually run by the party. Take a look at the USSR. That was also a socialist economy and was run by the Communist Party, not the people.
The workers might only own a small portion, but they would have power through voting. Just because something is run by the government doesn't mean that it is socialist. Nazi Germany had a few nationalized industries, but that doesn't make it socialist. The power of the government was centered in a few individuals. It was an authoritarian government. Same with the USSR - not really communist; the Soviet elites were the ones running the country and in control of industry, not the people.
Where do you get this vision a socialist state is anything but what you just described? Are you under the impression what we have in Europe is socialism? Talk about revisionist history. The ultimate socialist state was the USSR. You telling me they didnt have re-education camps? They didnt slaughter their own people? They didnt crush workers and people's rights? They didnt have a police state? And no nationalism????
Hitler like most fascists started off as a socialist. But was pragmatic enough to understand if you want an economy to function private industry would be required. Also, his situation was a bit more complicated as he was working within a democratic system to gain power. Unlike other communists\socialists who used revolution. He bartered with private industry for support.
Mussolini also started off as a socialist. This is why fascism and socialism are damn close on everything except on how to run an economy. Socialists want public owned industry, facists want a mixed economy with huge govt oversight and intervention where they please. But the police state, the one party state, the crushing power of govt are within both ideologies.
The USSR was not a socialist state. It was an authoritarian state. Socialism and the police state do not go hand in hand. Police states and dictatorial control go hand in hand with the fascist, authoritarian state.