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Section Daily Prep 4
You will review some of our discussion of the structure of cyclic groups from class on Tuesday and begin to unpack the idea of a permutation group via some examples.
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.
Determine the subgroups of a given order in a cyclic group.
State and instantiate the definitions of: permutation, permutation group, symmetric group.
Compose permutations in a permutation group.
Subsection Resources for Learning
Use these resources to prepare for class and answer the questions below.
Review Ch. 4 and the class notes as needed.
Gallian, Chapter 5, pp. 99-101
Figure 33. Reference Video for Symmetric Groups
Subsection Important Terms
Definition 34 . Permutation.
A
permutation on a set
\(A\) is a bijection from
\(A\) to itself.
Definition 35 . Permutation Group.
A
permutation group is a set of permutations on a set
\(A\) that forms a group under function composition.
Definition 36 . Symmetric Group.
The
symmetric group \(S_n\) is the set of all permutations on
\(\{1,2,\dots,n\}\text{.}\)
