MT423A: Abstract Algebra I
Study Guide for Final Exam
Chapters 0 through 8 and Chapters 12 and 13 in
Gallian
You are expected to be familiar with the contents of chapters 0 through 8,
12 and 13 in Gallian. Even if a term does not appear on the list below, you may
still need to know it for some of the problems.
Terms
You will be asked to explicitly state the definitions for some of the terms below.
The definitions do not need to be written down in formal book terminology, but
they need to be complete and correct.
1. divisor
2. multiple
3. prime
4. greatest common divisor and relatively prime
5. least common multiple
6. a mod n=r
7. group
8. Abelian group
9. order of a group
10. order of an element
11. subgroup
12. permutation of
A
13. permutation group of
A
14. bijection
15. symmetric group of degree
n
1
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16. even and odd permutations
17. alternating group of degree
n
18. group isomorphism
19. automorphism
20. inner automorphism induced by
a
21. coset of
H
in
G
22. stabilizer of a point
23. orbit of a point
24. external direct product
25. ring
26. subring
27. zero divisor
28. integral domain
29. field
30. characteristic of a ring
Problems
The problems on the midterm exam will come from the following list.
They
may be modified in the sense that some numbers or objects may be changed
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 Winter '11
 PhanThuongCang
 Abelian group, Subgroup, Cyclic group

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