We study the existence of many nonclosed pure subgroups of nondiscrete locally compact abelian groups. It is shown that every nondiscrete locally compact abelian group has uncountably many nonclosed pure subgroups. This in particular solves a question of Armacost. It is also shown that, if
G
G
is a nondiscrete locally compact abelian group and if either
G
G
is a compact group or the torsion part
t
(
G
)
t\left ( G \right )
of
G
G
is nonopen, then
G
G
has
2
c
{2^c}
proper dense pure subgroups, where
c
c
denotes the power of the continuum. This in particular gives a partial answer to another question of Armacost.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.