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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