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
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