A Structure result for bricks in Heisenberg groups

Norbert Hegyvári (1) , François Hennecart (2)

1 institute of Mathematics [Budapest]
2 ICJ - Institut Camille Jordan

We show that for a sufficiently big \textit{brick} $B$ of the $(2n+1)$-dimensional Heisenberg group $H_n$ over the finite field $\mathbb{F}_p$, the product set $B\cdot B$ contains at least $|B|/p$ many cosets of some non trivial subgroup of $H_n$.

Domaines: Théorie des nombres [math.NT]

Norbert Hegyvári, François Hennecart. A Structure result for bricks in Heisenberg groups. Journal of Number Theory, 2013, 133 (9), pp.2999-3006. ⟨10.1016/j.jnt.2013.03.011⟩. ⟨hal-00868107⟩