Specht and dual Specht filtrations of p-permutation KS2p-modules

We consider the p-permutation KS2p-modules for p=charK an odd prime. For each such module we determine whether it possesses a Specht filtration, and also whether it possesses a dual Specht filtration. Some of those modules are shown to have one of the above filtrations and not the other, some to have both, and some none. When the vertex of the module is generated by p-cycles we give a detailed proof. The other case is stated, and covered in the author's thesis. Lastly we extend our results to the p-permutation modules whose vertex is a subgroup of S2p for other symmetric groups.