locally $𝒫$

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

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 $𝒫$
Canonical name	LocallycalP
Date of creation	2013-03-22 14:18:57
Last modified on	2013-03-22 14:18:57
Owner	yark (2760)
Last modified by	yark (2760)
Numerical id	5
Author	yark (2760)
Entry type	Definition
Classification	msc 20E25
Related topic	GeneralizedCyclicGroup
Related topic	LocallyFiniteGroup
Related topic	LocallyNilpotentGroup