  Furstenberg and Glasner proved that for an arbitrary k in N, any piecewise
syndetic set contains k length arithmetic progression and such collection is
also piecewise syndetic in Z: They used algebraic structure of beta N. The
above result was extended for arbitrary semigroups by Bergelson and Hindman,
again using the structure of Stone-Cech compactification of general semigroup.
However they provided the abundances for various types of large sets. But the
abundances in in many large sets is still unknown. In this work we will provide
the abundance in Quasi Central sets, J-sets and C-sets.
