Introduction

Pinter will introduce the basic categories of abstract algebra: groups, rings and fields. The book works all the way to Galois Theory, which is proving that the quintic is not solvable using radicals. A lot of the good stuff is in the exercises, while the theory contains the bare essentials. This makes the book very close to a problem based course.

Problem List

Chapter 2: Operations

A F
B F
D A

Chapter 3: The Definition of Groups

A12 F
B1 F
C F
D F
F A
G A

Chapter 4: Elementary Properties of Groups

A C
B F
C F
D1238 F
E F
F F
G F
H12 F

Chapter 5: Subgroups

A17 F
B1 F
B45 F
C128 F
D12358 F
E C
F1 C
G14 C
H A

Chapter 6: Functions

C F
H A
I A

Chapter 7: Groups of Permutations

A C
D F
E F
F C

Chapter 8: Permutations of a Finite Set

A1(a),2(a), 3(ab), 4(a), 5 C
B1(a) C
B38 F
C1 C
C234 F
D12 F
E F
F123 F
G F
H F

Chapter 9: Isomorphism

A F
B F
C C
D12 F
E1 F
H F
I34 F

Chapter 10: Order of Group Elements

A F
B C
C F
D1 F

Chapter 11: Cyclic Groups

A C
B12 F
C12 F
D123 F

Chapter 12: Partitions and Equivalence Relations

D F

Chapter 13: Counting Cosets

A34 C
B17 F
C123 F
D1 F
E123 F
F F
G F
H F
I F
K A

Chapter 14: Homomorphisms

A F
B1 F
C F
D F
E1 F
F1 F
G F
H F
I F

Chapter 15: Quotient Groups

A123 F
D3 F
F F
G F
H F

Chapter 17: The Fundamental Homomorphism Theorem

A12 F
B1 F
E F
F F
H F
I F
J F
K F
L F
M F
N F
O F
P F
Q F