Poly-(cyclic or finite) group
= Poly-(cyclic or finite) group
A group is poly-(cyclic or finite) when it has a finite <subnormal series> $1=G_0\triangleleft G_1\triangleleft\cdots\triangleleft G_r=G$ in which each quotient $G_i/G_{i-1}$ is a <cyclic group> or a <finite group>. Each term need only be normal in the next term. The <polycyclic group> condition instead requires every factor to be cyclic.