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a ☆ (b ☆ c)=(a ☆ b) ☆ c

(2) there is unitary e∈G,

a ☆ e = e ☆ a = a

③ Any element X in G has an inverse element X? 1∈G，

a- 1 ☆ a = a ☆ a- 1 = e

Then it's called

Set < g, ☆ > Is a group, if the operation satisfies the commutative law,

a ☆ b = b ☆ a

Then it's called

For example. < Z，+>，& ltq，+& gt； ，& ltr，+& gt； ,< zinc,+n > ("+"is a common addition; "+n" is the addition of modules) is a commutative group.