Statements (59)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:group_of_people
|
| gptkbp:actsOn |
unit interval [0,1]
|
| gptkbp:definedIn |
piecewise linear homeomorphisms of [0,1] with breakpoints at dyadic rationals and slopes powers of 2
|
| gptkbp:hasProperty |
not automatic
not residually finite not elementary amenable every proper quotient is abelian has exponential growth has infinite cohomological dimension has infinite presentation has no non-abelian finite quotients has no non-trivial center has no non-trivial finite index subgroups has no non-trivial finite quotients has solvable conjugacy problem has solvable word problem is Hopfian is not Kazhdan is not amenable (open) is not locally finite is not virtually Coxeter is not virtually Hopfian is not virtually Kazhdan is not virtually abelian is not virtually amenable (open) is not virtually automatic is not virtually cyclic is not virtually free is not virtually lattice is not virtually linear is not virtually nilpotent is not virtually residually finite is not virtually simple is not virtually solvable is not virtually surface is not virtually torsion-free not a Coxeter group not a free group not a lattice in a Lie group not a surface group not amenable (open problem) not known to be amenable or non-amenable not linear not simple has no non-trivial finite-dimensional linear representations |
| gptkbp:hasSubgroup |
gptkb:Thompson_group_T
gptkb:Thompson_group_V |
| https://www.w3.org/2000/01/rdf-schema#label |
Thompson group F
|
| gptkbp:namedAfter |
gptkb:Richard_J._Thompson
|
| gptkbp:presentedBy |
generators x_0, x_1 with certain relations
|
| gptkbp:type |
infinite group
torsion-free group finitely presented group finitely generated group non-amenable group (open problem) non-elementary amenable group piecewise linear group |
| gptkbp:bfsParent |
gptkb:Thompson_group
|
| gptkbp:bfsLayer |
5
|