Group theory
Provisional editorial order for Top Open Problems: Millennium Prize Problems first, followed by assessed difficulty tiers; the unassessed remainder keeps its previous catalogue order. About rankings
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- Math-24 Inverse Galois Problem
- Math-118 Residual Finiteness of Hyperbolic Groups
- Math-149 Serre's congruence subgroup conjecture
- Math-168 Hyperlinearity of Every Group
- Math-225 Wall's Poincare Duality Group Conjecture
- Math-227 Babai's Diameter Conjecture for Finite Simple Groups
- Math-245 K(pi,1) conjecture for Artin groups
- Math-282 Alperin–McKay Conjecture
- Math-285 Complex linearity of closed-surface mapping class groups by genus
- Math-286 Grigorchuk Gap Conjecture
- Math-308 Amenability of Thompson's Group $F$
- Math-317 Tits Alternative for CAT(0) Groups
- Math-327 Gromov's Surface Subgroup Question for One-Ended Hyperbolic Groups
- Math-341 Broué's Abelian Defect Group Conjecture
- Math-347 Congruence Subgroup Property for Mapping Class Groups of Surfaces of Genus at Least Three
- Math-355 Arithmeticity of Lattices in PU(n,1) for n at Least 4
- Math-378 Growth of finitely presented groups
- Math-398 Margulis–Platonov normal-subgroup conjecture
- Math-429 Lück's Determinant Conjecture for Discrete Groups
- Math-501 Quillen's $p$-Subgroup Conjecture
- Math-504 CAT(0) Actions of Artin Groups
- Math-1147 Which lattices occur as intervals in subgroup lattices of finite groups?
- Math-1188 Kourovka Notebook Problem 21.1
- Math-1189 Kourovka Notebook Problem 21.2
- Math-1190 Kourovka Notebook Problem 21.3
- Math-1191 Kourovka Notebook Problem 21.4
- Math-1192 Kourovka Notebook Problem 21.5
- Math-1193 Kourovka Notebook Problem 21.7
- Math-1194 Kourovka Notebook Problem 21.9
- Math-1195 Kourovka Notebook Problem 21.11
- Math-1196 Kourovka Notebook Problem 21.13
- Math-1197 Kourovka Notebook Problem 21.16
- Math-1198 Kourovka Notebook Problem 21.17
- Math-1199 Kourovka Notebook Problem 21.19
- Math-1200 Kourovka Notebook Problem 21.20
- Math-1201 Kourovka Notebook Problem 21.22
- Math-1202 Kourovka Notebook Problem 21.23
- Math-1203 Kourovka Notebook Problem 21.25
- Math-1204 Kourovka Notebook Problem 21.26
- Math-1205 Kourovka Notebook Problem 21.27
- Math-1206 Kourovka Notebook Problem 21.28
- Math-1207 Kourovka Notebook Problem 21.30
- Math-1208 Kourovka Notebook Problem 21.31
- Math-1209 Kourovka Notebook Problem 21.34
- Math-1210 Kourovka Notebook Problem 21.35
- Math-1211 Kourovka Notebook Problem 21.39
- Math-1212 Kourovka Notebook Problem 21.40
- Math-1213 Kourovka Notebook Problem 21.41
- Math-1214 Kourovka Notebook Problem 21.42
- Math-1215 Kourovka Notebook Problem 21.45