Math 301 §A: Objectives for Final Exam
This document incorporates the Objectives for the First
Midterm Exam, the Objectives for the Second Midterm
Exam and the Objectives for the Third Midterm
Exam.
State the Definitions and use them in Proofs.
- Conjugacy class of a group element
- Conjugate subgroups
- Sylow p-subgroup
- Group action on a set
- Normalizer of a subgroup
- Set of elements fixed by a permutation
State the Theorems and use them in Proofs.
- Orbit-Stabilizer Theorem and its realizations
- Number of conjugates of a group element
- Subgroups conjugate to a given subgroup
- The Class Equation
- p-groups have nontrivial centers
- Groups of order p2 are Abelian
- The Sylow Theorems
- Cauchy's Theorem
- Condition for a group of order pq to be cyclic
- (not-) Burnside's Theorem
