Definition

Group (G, *) is a set G, together with a binary operation * on G, such that the following axioms are satisfied:

  • The bianary operation * is associative
  • There is an element e in G such that e * x = x * e = x for all x € G. (This element e is an identity element for * on G)
  • For each a an G, there is an element a’ is an inverse of a with the property that a’ * a = a * a’ = e

Note:

Many books have another axiom for a group, namely that G is closed under the operation *, that is (a*b) € G for all a, b € G

About erfanmath

Erfan adalah guru matematika di SMA Unggulan BPPT Darus Sholah Jember dan juga sebagai pembimbing olympiade matematika SD, SMP, dan SMA

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