Algebra/Chapter 27/Groups

------------------------ AlgebraChapter 27: Group TheorySection 3: Groups Lagrange's Theorem 1.25rem 27.3: Groups Definition of a Group In standard terms, a group G is a set equipped with a binary operation • such that the following properties hold: The binary operation is closed. That means, for any two values a and b in G, the combined value a • b is also in G. The binary operation is associative. For any values a, b, c in G, a • (b • c) = (a • b) • c. There exists a unique identity element e in G such that for all values a in G, a • e = a = e • a. There exists a unique inverse element such that If the binary operation is commutative, or b • a = a • b, then the group is said to be Abelian.