Index

·, 104

≡, 13

∼,

=

60, 141

∼σ, 91

≤, 51

, 70

0G, 34

0R, 131

1G, 35

1R, 131

{1,. . . ,

n}σ,

91

, 32

n

k=1

ak, 6

Gi, 54

Ri, 135

Gi, 54

a ∗ b, 33

a + S, 67

−a, 34

a˜b, 25

a−1,

35

a, 14

a | b, 5

aS, 67

(a), 143, 150

(a, b), 5

(

a

p

)

, 189

[a]n, 14

[a, b], 13, 183

[a], 14, 25

A/˜, 25

An, 97

A\B, 2

A × B, 21

|A|, 4

Aut(G), 62, 66

abelian, 46

abelian extension, 247

ACC, 182

ACCP, 177

action, 103

additively, 34

adjoining, 197

aﬃne motion, 45

algebraic, 197

algebraic closure, 204, 210

algebraic extension, 197

algebraic integer, 182

algebraic numbers, 182, 204

algebraically closed, 210

algebraically independent, 204

alternating group, 97

alternating n-form, 102

annihilator, 149

antisymmetric, 209

ascending chain condition on ideals, 182

ascending chain condition on principal

ideals, 177

associate, 169

associated partition, 94

automorphism, 60, 141

automorphisms of An, 102

automorphisms of Sn, 101

Axiom of Choice, 214

Bij(X), 110

base m, 11

basis, 194

bijection, 21

bijective, 60, 141

binary operation, 33

Binet’s formula, 10

binomial coeﬃcient, 10

Binomial Theorem, 10

Boolean, 139

bounded above, 1

bounded below, 2

Burnside, 240

Burnside’s Orbit Counting Theorem, 108

cg, 62

ch, 94

C∞(R), 45

C0(R),

45

C, 35

char R, 138, 215

cor(H), 78

251