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Section Daily Prep 2
You will review some of the basic computations and definitions we worked on in class on Tuesday. You will also learn about some elementary properties of groups relating to uniqueness and cancellation.
Objectives: Basic Learning Objectives
Before our class meeting, you should use the resources below to be able to learn the following. You should be reasonably fluent with these; we’ll answer some questions on them in class but not reteach them in detail.
State and instantiate the definitions of: binary operation, group, Abelian group
Determine whether a set with a given binary operation is or is not a group
Given a group, identify its identity element; identify the inverse of a given element; perform operations in the group.
State the following mathematical results: Theorem 2.1, 2.2, 2.3 from Gallian
Subsection Resources for Learning
Use these resources to prepare for class and answer the questions below.
Gallian, Chapter 2, pp. 50-51
Review class notes and the rest of Chapter 2 as needed.
Figure 9. Reference Video for Group Basics
Subsection Important Terms
Definition 10 . Binary Operation.
Let
\(G\) be a set. A
binary operation on
\(G\) is a function that assigns each ordered pair of elements of
\(G\) an element of
\(G\text{.}\)
Definition 11 . Abelian group.
A group
\((G,\circ)\) is called an
Abelian group if the operation is commutative; that is,
\(ab=ba\) for all
\(a,b\in G\text{.}\)
