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Chapter 14 Groups
Objectives
Reproduce the definition of a group.
Recognize whether a set with a given binary operation is a group.
Compute with elements in a group.
Find the identity element of a group.
Find the inverse of an element in a group.
Recognize whether a set with modular multiplication is a group.
A group is a simple mathematical structure made of a set and a binary operation on that set. The operation has the properties studied in the previous section. Groups appear in many areas of mathematics and describe symmetries in fields such as chemistry and physics. We define groups, give examples of groups, and introduce two collections of infinitely many groups.
