# locally $\cal P$

Let $\cal P$ be a property of groups. A group $G$ is said to be locally $\cal P$ if every nontrivial finitely generated subgroup of $G$ has property $\cal P$.

For example, the locally infinite groups are precisely the torsion-free groups. Other classes of groups defined this way include locally finite groups and locally cyclic groups.

Title locally $\cal P$ LocallycalP 2013-03-22 14:18:57 2013-03-22 14:18:57 yark (2760) yark (2760) 5 yark (2760) Definition msc 20E25 GeneralizedCyclicGroup LocallyFiniteGroup LocallyNilpotentGroup