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A society is a group of humans that form a semi-closed system, in which most interactions are with other people belonging to the group. A society is a network of relationships between people. A society is an interdependent community.
The name was historically applied to the community formed by all the nationals of a country - a questionable idea now thanks to globalization. Some, like Margaret Thatcher, deny they exist at all. Societies are the main subject of study of social sciences.
Also, some groups apply the title "society" to themselves, as the "American Society of Mathematics". This is most common in commerce, in which a partnership between investors to start a business is usually called a "society".
See evolution of societies, Information society, social capital