  Furstenberg and Glasner proved that for an arbitrary k in N, any piecewise
syndetic set contains k term 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.
Beiglbock provided an elementary proof of the above result and asked whether
the combinatorial argument in his proof can be enhanced in a way which makes it
applicable to a more abstract setting. In this work we provide a positive
answer to Beiglbock question for commutative semigroup.
