Throughout the question, let denote a set together with a binary operation on it. The below is the standard definition of a group structure on that I first saw:
(G1)
$x \cdot(y\cdot ...

Throughout the question, let X denote a set together with a binary operation ⋅ on it. The below is the standard definition of a group structure on X that I first saw:
(G1)
$x \cdot(y\cdot ...