Non-commutative and polynomial multidimensional stronger central sets theorem

The Central Sets Theorem and Milliken-Taylor Theorem extends the famous Hindman?s theorem in two different directions. In [1] Beiglboeck proved a joint extension of these two theorems. In this article, we prove the non-commutative version of Beiglboeck?s result. Then we also prove the polynomial extension of stronger Central Sets Theorem for general commutative groups, which extents a recent result of [6].