Chapter 14 Groups
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.
Groups are simple mathematical structures that only consist of a set and a binary operation on that set with certain properties, namely those that we investigated in the previous section. Groups can be found in many areas of mathematics and are used to describe symmetries in other fields such as chemistry and physics. We define groups, give examples of groups, and introduce two collections of infinitely many groups.