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Mnementh said:

"Socialism is an economic and political philosophy encompassing diverse economic and social systems characterised by social ownership of the means of production, as opposed to private ownership."

https://en.wikipedia.org/wiki/Socialism

That is pretty independent from the existence of state. Basically it means factories aren't privately owned. The actual socialist countries in the last century implemented that by state ownership of factories. There are other possibilities, like a cooperative.

Some socialists will argue that the State exists solely to protect the ruling class, and that without there being a ruling class, the state is no longer necessary. 

I'm not saying that the actual definition requires it, but some people have the opinion that it does. And on the other end of it, as Zorg pointed out that some conservatives frequently feel that any economic policy they disagree with is socialism.