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Wikipedia states that van Dyck (1882) was the first to give the definition of a group in the modern way. Before this, what were some of the original axioms or conditions for groups? I mean, how were groups originally defined/restricted? I understand groups were originally studied as groups of permutations, but that is all I know.

Thanks.

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The Wikipedia page looks pretty complete to me.

Like all other main concepts in mathematics, it took time for a precise definition of a group to arise; it was never axiomatized from the start.

See also the book A History of Abstract Algebra and the articles The Foundation Period in the History of Group Theory and The Evolution of Group Theory: A Brief Survey.

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  • $\begingroup$ Thanks for the extra links. That last article is a great, relaxing read and answers my question to a tee. $\endgroup$
    – Sephra
    May 14, 2013 at 1:57

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