= Restricted direct sum of groups
{title2=$\bigoplus_iG_i$}
The restricted direct sum of a family of <groups> $G_i$ is the subgroup of their <direct product of groups> consisting of tuples with only finitely many nonidentity coordinates. Multiplication is coordinatewise. If every factor is a <finite group>, each <subgroup> that is a <finitely generated group> lies in a finite subproduct, so the restricted direct sum is a <locally finite group>. This gives concrete infinite <torsion groups> without a uniform bound on element orders.
Back to article page
