Residually cyclic group

Definition
A group is termed residually cyclic if it satisfies the following equivalent conditions:


 * 1) For every non-identity element, there is a defining ingredient::normal subgroup of finite index of the whole group not containing that element, such that the quotient group is a cyclic group.
 * 2) The group is isomorphic to a defining ingredient::subdirect product of cyclic groups.
 * 3) The group can be embedded as a subgroup in a direct product of cyclic groups.