MATH 417 Midterm 1 Study Guide
The main focus of the exam is on chapters 2, 3, and 4. Make sure you are familiar with the material
in Chapter 0 but Chapter 0 was supposed to be a review of things you already knew so it will not
be the main focus of the questions on the exam.
•
Deﬁnitions you should know:
–
Binary operation
–
Group
–
Abelian group
–
Order of a group
–
Order of an element
–
Subgroup of a group
–
Trivial subgroup
–
Proper subgroup
–
Cyclic subgroup
–
Generator of a cyclic subgroup
–
Center of a group
–
Centralizer of an element of a group
•
Theorems you should know the statements of and be able to use:
–
Theorem 2.1(*)
–
Theorem 2.2 (*)
–
Theorem 2.3 (*)
–
Theorem 3.1 OneStep Subgroup Test
–
Theorem 3.2 TwoStep Subgroup Test
–
Theorem 3.4
< a >
Is a Subgroup (*)
–
Theorem 3.5 Center is a Subgroup (*)
–
Theorem 3.6
C
(
a
) is a Subgroup (*)
–
Theorem 4.1 (I presented this diﬀerently in lecture)
–
Corollary 1 of 4.1

a

=
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '08
 Wilson
 Math, Subgroup, Cyclic group, cylic group

Click to edit the document details