This is a review paper on the generalization of Euclidean as well pseudo-Euclidean groups interest in quantum mechanics. The Weyl–Heisenberg groups, Hn, together with Euclidean, En, and Ep,q, are two families particular due to their applications physics. In present manuscript, we show that, together, they give rise more general family Kp,q, that contain Hp,q Ep,q subgroups. It noteworthy proper...

Suppose that A , B and S are non-empty subsets of a finite abelian group G with | > 1 . Then the generalized restricted sumset + : = { b ∈ − ∉ } contains at least min ⁡ 3 p ( ) elements, where is prime factor Further, we also have ≥ 2 provided both large respect to