In the mathematical field of group theory, a group G is residually finite or finitely approximable if for every element g that is not the identity in G...

{\displaystyle \eta } is injective if and only if the group G {\displaystyle G} is residually finite (i.e., ⋂ N = 1 {\displaystyle \bigcap N=1} , where the...

minimal residual method Residual set, the complement of a meager set Residual property (mathematics), a concept in group theory Residually finite group, a...

of non-Hopfian groups. The groups contain residually finite groups, Hopfian groups that are not residually finite, and non-Hopfian groups. Define A = (...

Q of rationals. Any finitely generated residually finite group. Any word-hyperbolic group. Quasicyclic groups. The additive group R of real numbers. The...

absolutely presented groups, including: Finitely presented simple groups. Finitely presented residually finite groups One relator groups (this is a theorem...

generalization of amenable and residually finite groups. The name "sofic", from the Hebrew word סופי meaning "finite", was later applied by Weiss (2000)...

infinite groups they are distinguished by many remarkable properties. Finitely generated linear groups have the following properties: They are residually finite;...

surjunctive groups include all locally residually finite groups, all free groups, all subgroups of surjunctive groups, all abelian groups, all sofic groups, and...

from G to some group H with property X. Important examples include: Residually finite Residually nilpotent Residually solvable Residually free Marshall...