Editing Locally cyclic group (section)

==Examples of locally cyclic groups that are not cyclic==
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| The additive group of [[rational number]]s ('''Q''', +) is locally cyclic – any pair of rational numbers ''a''/''b'' and ''c''/''d'' is contained in the cyclic subgroup generated by 1/(''bd'').{{sfnp|Rose|2012|p=52}}
| The additive group of the [[dyadic rational number]]s, the rational numbers of the form ''a''/2<sup>''b''</sup>, is also locally cyclic – any pair of dyadic rational numbers ''a''/2<sup>''b''</sup> and ''c''/2<sup>''d''</sup> is contained in the cyclic subgroup generated by 1/2<sup>max(''b'',''d'')</sup>.
| Let ''p'' be any prime, and let ''μ''<sub>''p''<sup>∞</sup></sub> denote the set of all ''p''th-power [[root of unity|roots of unity]] in '''C''', i.e.
: <math>\mu_{p^\infty} = \left\{\exp\left(\frac{2\pi im}{p^k}\right) : m, k \in \mathbb{Z}\right\}</math>

Then ''&mu;''<sub>''p''<sup>&infin;</sup></sub> is locally cyclic but not cyclic. This is the [[Prüfer group|Prüfer ''p''-group]]. The Prüfer 2-group is closely related to the dyadic rationals (it can be viewed as the dyadic rationals modulo 1).
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