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A characterization of generalized quaternion 2-groups. (English) Zbl 1205.20024
It is shown that the cyclic \(p\)-groups of order at least \(p^2\) and the generalized quaternion groups are the only finite groups having a nontrivial cyclic subgroup that contains or is contained in every other cyclic subgroup.

MSC:
20D30 Series and lattices of subgroups
20D15 Finite nilpotent groups, \(p\)-groups
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