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Closure

For all a, b in G, the result of the operation a • b is also in G.b[›]

Associativity

For all a, b and c in G, the equation (a • b) • c = a • (b • c) holds.

Identity element

There exists an element e in G, such that for all elements a in G, the equation e • a = a • e = a holds.

Inverse element

For each a in G, there exists an element b in G such that a • b = b • a = e, where e is the identity element.