On Pro-p Cappitt Groups with finite exponent

A pro-p Cappitt group is a pro-p group G such that S ˜(G)=〈L⩽ c G|L⋪G〉 ¯ is a proper subgroup (i.e. S ˜(G)≠G). In this paper we prove that non-abelian pro-p Cappitt groups whose torsion subgroup is closed and it has finite exponent. This result is a natural continuation of main result of the first author [7]. 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 (see Theorem 1 and Lemma 7 in [1]).