locally 𝒫

Let 𝒫 be a property of groups. A group G is said to be locally 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