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 = (...

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

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

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

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

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

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

result: The mapping class group is residually finite. The proof proceeds first by using residual finiteness of the linear group Sp 2 g ⁡ ( Z ) {\displaystyle...

G. Every finite p-group is nilpotent. The remainder of this article deals with finite p-groups. For an example of an infinite abelian p-group, see Prüfer...

the finiteness properties of polycyclic groups; for example, they satisfy the maximal condition, and they are finitely presented and residually finite. In...

there exists a hyperbolic group which is not residually finite. Non-elementary (infinite and not virtually cyclic) hyperbolic groups have always exponential...

subgroups in an arithmetic group provides it with a wealth of subgroups, in particular it shows that the group is residually finite. An important question...

further below. As a corollary, if the index of H in G is 2, or for a finite group the lowest prime p that divides the order of G, then H is normal, as...

word-hyperbolic group. Being a torsion-free group. Being a polycyclic group. Being a group with a solvable word problem. Being a residually finite group. Being...

tilings, and non-residually finite groups. Wise's research has focused on the role of non-positively curved cube complexes within geometric group theory and...

G_{\omega }\neq G_{n}} for all finite n, then G / G ω {\displaystyle G/G_{\omega }} is not nilpotent, but it is residually nilpotent. There is no general...

non-elementary Kleinian groups which are determined by their finite quotients among finitely generated residually finite groups. He has published more...

he proved that this group is infinite, periodic and residually finite. In a subsequent 1984 paper Grigorchuk proved that this group has intermediate growth...

poker). A population with finitely many values N {\displaystyle N} in the support of the population distribution is a finite population with population...

language is defined as a (finite or infinite) set of strings that can be described by one of the mathematical formalisms called "finite automaton", "regular...

generated). Similarly such a monoid is residually finite if and only if all of its Schützenberger groups are residually finite. Brandon, Robert; Hardy, Darel;...

subgroup theorem describes the fusion of elements in a Sylow subgroup of a finite group. The focal subgroup theorem was introduced in (Higman 1953) and is the...

solvable groups), since their group algebras are known to be Ore domains. It follows that the conjecture holds more generally for all residually torsion-free...

multiply connected space like a 3 torus has everywhere zero curvature but is finite in extent, whereas a flat simply connected space is infinite in extent (such...

closed subgroups of finite index, so that the discrete quotient group is always finite. Alternatively, one can define a pro-p group to be the inverse limit...

Invent. Math. 219, 1009–1068 (2020). Dawid Kielak. Residually finite rationally solvable groups and virtual fibring. J. Amer. Math. Soc. 33, 451-486...

in a group G contains a normal subgroup N also of finite index in G, it easily follows that: If a group G is SQ-universal then so is any finite index...