# Changes

## Locally cyclic group

, 14:53, 16 April 2017
no edit summary
{{group property}}
{{lattice-determined group property}}
==Definition==
|-
| [[dissatisfies metaproperty::finite direct product-closed group property]] || No || See next column || It is possible to have groups $G_1, G_2$ such that both $G_1$ and $G_2$ are locally cyclic but the [[external direct product]] $G_1 \times G_2$ is not locally cyclic. In fact, ''any'' choice of nontrivial $G_1, G_2$ gives an example.
|-
| [[satisfies metaproperty::lattice-determined group property]] || Yes || See next column || Given two [[lattice-isomorphic groups]] $G_1, G_2$, either both $G_1$ and $G_2$ are locally cyclic or neither is. The explicit condition for being locally cyclic is that the lattice of subgroups is distributive.
|}