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Locally cyclic group

41 bytes added, 14:59, 16 April 2017
Metaproperties
| [[dissatisfies metaproperty::finite direct product-closed group property]] || No || See next column || It is possible to have groups <math>G_1, G_2</math> such that both <math>G_1</math> and <math>G_2</math> are locally cyclic but the [[external direct product]] <math>G_1 \times G_2</math> is not locally cyclic. In fact, ''any'' choice of nontrivial <math>G_1, G_2</math> gives an example.
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| [[satisfies metaproperty::lattice-determined group property]] || Yes || See next column [[locally cyclic iff distributive lattice of subgroups]] || Given two [[lattice-isomorphic groups]] <math>G_1, G_2</math>, either both <math>G_1</math> and <math>G_2</math> are locally cyclic or neither is. The explicit condition for being locally cyclic is that the lattice of subgroups is distributive.
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