Scrabble?! RESIDUALLY

Definitions of RESIDUALLY in various dictionaries:

In the mathematical field of group theory, a group G is residually finite or finitely approximable if for every nontrivial element g in G there is a homomorphism h from G to a finite group, such that h ( g ) ≠ 1. {\displaystyle h(g)\neq 1.\,} There are a number of equivalent definitions: A group is residually finite if for each non-identity element in the group, there is a normal subgroup of finite index not containing that element. A group is residually finite if and only if the intersection of all its subgroups of finite index is trivial. A group is residually finite if and only if the intersection of all its normal subgroups of finite index is trivial. A group is residually finite if and only if it can be embedded inside the direct product of a family of finite groups.