Editing Glossary of group theory (section)

== L ==
{{glossary}}
{{term|1=lattice of subgroups}}
{{defn|1=The [[lattice of subgroups]] of a group is the [[Lattice (order)|lattice]] defined by its {{gli|subgroup|subgroups}}, [[Partially ordered set|partially ordered]] by [[set inclusion]].}}
{{term|1=locally cyclic group}}
{{defn|1=A group is [[locally cyclic group|locally cyclic]] if every {{gli|finitely generated group|finitely generated}} subgroup is {{gli|cyclic group|cyclic}}. Every cyclic group is locally cyclic, and every {{gli|finitely generated group|finitely-generated}} locally cyclic group is cyclic. Every locally cyclic group is {{gli|abelian group|abelian}}. Every {{gli|subgroup}}, every {{gli|quotient group}} and every {{gli|group homomorphism|homomorphic}} image of a locally cyclic group is locally cyclic.}}
{{glossary end}}