Finite residual
= Finite residual
{title2=$R_G=\bigcap_{N\triangleleft G,\ [G:N]<\infty}N$}
The finite residual consists of all elements killed by every <homomorphism> to a <finite group>. A <group> is a <residually finite group> precisely when its finite residual is trivial. Intersecting all finite-index <subgroups> gives the same result: the <normal core> of each such <subgroup> is normal of finite index and lies inside it.