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I have a question related to Group Theory and its interpretation from a social point of view.

if we suppose, that a group of Humans can be considered as an algebraic structure : a group (G,◦) with a set of elements and a set of axioms like closure, associativity, identity and invertibility.

How can we describe ◦ and the axioms in term of interactions and relations between humans (socially)

I was wondering if someone can give me an idea about this subject, or some pointers if it was already treated.

Thank you.