Associativity, For all a, b, c, in G, one has ( a*b )*c = a*( b*c ), Identity element, An element e in G such that e*a = a and a*e = a, Inverse element, For each a in G, there exists an element b in G such that a*b = e and b*a = e, where e is the identity element., Abelian group, A group, where for each a and b in G, the equation a*b=b*a is true, Non-abelian group, A group, where for each a and b in G, the equation a*b=b*a is false, Order of group, The number of elements of G, Order of an element, The smalles positive integer n such that an=e, Symmetric group, Group of bijections or permutations
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