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.
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.