locally cyclic group is a group (G, *) in which every finitely generated subgroup is cyclic. Every cyclic group is locally cyclic, and every locally cyclic...

In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused...

element is called cyclic. Every infinite cyclic group is isomorphic to the additive group of the integers Z. A locally cyclic group is a group in which every...

subgroup is cyclic. Every cyclic group is locally cyclic, and every finitely-generated locally cyclic group is cyclic. Every locally cyclic group is abelian...

number theory, locally compact abelian groups are abelian groups which have a particularly convenient topology on them. For example, the group of integers...

In abstract algebra, every subgroup of a cyclic group is cyclic. Moreover, for a finite cyclic group of order n, every subgroup's order is a divisor of...

abelian group Group representation Klein four-group List of small groups Locally cyclic group Nilpotent group Non-abelian group Solvable group P-group Pro-finite...

{Z} ,n\in \mathbb {N} .} Hausdorff completion Locally cyclic group Pro-p group – type of profinite groupPages displaying wikidata descriptions as a fallback...

locally finite group is a group for which every finitely generated subgroup is finite. Since the cyclic subgroups of a locally finite group are finitely...

integers (with the addition operation) is the "only" infinite cyclic group. Some groups can be proven to be isomorphic, relying on the axiom of choice...