  A pro-p Cappitt group is a pro-p group G such that the subgroup topologically
generated by all non-normal closed subgroups is a proper subgroup of G. In this
paper we prove that non-abelian pro-p Cappitt groups whose torsion subgroup is
closed has finite exponent. We also prove that in a pro-p Cappitt group its
subgroup commutator is a procyclic central subgroup. Finally we show that pro-2
Cappitt groups of exponent 4 are pro-2 Dedekind groups. These results are pro-p
versions of the generalized Dedekind groups studied by Cappitt.
