Index

C1,1

local group, 36

p-adic norm, 11

*-homomorphism, 146

A group is virtually nilpotent if it

contains a finite index subgroup

which is nilpotent., 21

abstract Lie algebra, 249

additive combinatorics, 14

adjoint representation, 44, 85

Ado’s theorem, 250

almost period, 179

approximate group, 162, 212

arrow’s theorem, 147

associated neighbourhood, 119

asymptotic notation, xiii, 159

baby Peter-Weyl theorem, 91

Baker-Campbell-Hausdorff formula, 43

Baker-Campbell-Hausdorff-Dynkin

formula, 48

Birkoff-Kakutani theorem, 101

Borel measure, 77

Brouwer fixed point theorem, 131

Burnside’s theorem, 235

cancellative local group, 118

Cartan’s theorem, 54

Cayley graph, 20

central element, 6

centraliser, 6

chain rule, 31

character, 304

characteristic subgroup, 240

cheap structure theorem, 210

class function, 304

classification of one-parameter

subgroups, 57

clopen set, 127

closed graph theorem, 57

cocompact subgroup, 94

cocompact topology, 61

cocycle, 280

cocycle equation, 280

cohomologous, 281

commutator, 6, 239

compact operator, 89

compact-open topology, 66

compactness of integral operators, 89

compactness theorem, 157

complete measure space, 313

concretely nilpotent Lie algebra, 254

conjugate, 239

connected component, 128

connected space, 127

continuous action, 127

convolution, 88

coset nilprogression, 165

coset progression, 17, 164

countable saturation, 151

degree, 291

derivation, 256

derivations and vector fields, 33

derivative map, 31

directional derivative, 32

335