Y.S.Han Finite fields 1 Groups Let G be a set of elements.A binary operation on G is a rule that assigns to each pair of elements a and b a uniquely defined third element c=a*b in G. A binary operation on G is said to be associative if,for any a, b,and c in G, a*(b*C)=(a*b)*c. A set G on which a binary operation is defined is called a group if the following conditions are satisfied: 1.The binary operation is associative. 2.G contains an element e,an identity element of G,such that,for any a∈G, a*e三e米a=a. 3.For any element a G,there exists another element a'G School of Electrical Engineering Intelligentization,Dongguan University of Technology Y. S. Han Finite fields 1 Groups • Let G be a set of elements. A binary operation ∗ on G is a rule that assigns to each pair of elements a and b a uniquely defined third element c = a ∗ b in G. • A binary operation ∗ on G is said to be associative if, for any a, b, and c in G, a ∗ (b ∗ c) = (a ∗ b) ∗ c. • A set G on which a binary operation ∗ is defined is called a group if the following conditions are satisfied: 1. The binary operation ∗ is associative. 2. G contains an element e, an identity element of G, such that, for any a ∈ G, a ∗ e = e ∗ a = a. 3. For any element a ∈ G, there exists another element a ′ ∈ G School of Electrical Engineering & Intelligentization, Dongguan University of Technology