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A group A is a set, combined with a binary operation *, which has 4 specific properties. COLUMN_START^ * Closure: * Associativity: * Identity: * Inverse: COLUMN_SPLIT^ The set A is closed The operation * is associative. A contains an identity element. For every element in A there exists an inverse element COLUMN_END These are called the group axioms. If the binary operation is also commutative (see commutative operation) then the group is called an Abelian Group or commutative group.